LIBRARY 

OF  THE 

UNIVERSITY  OF  CALIFORNIA. 

GIFT    OF 


Class 


MODEBN 


Commercial  Arithmetic 


BY 

F.  J.  SCHNECK 


CHICAGO 


POWERS  &  LYONS 

NEW  YORK  SAN  FRANCISCO 


APH    4    1911 
GIFT 


COPYRIGHT,  1902 

BY 
POWERS  &  LYONS 


" 


or -HE 
UNIVERSITY 

OF 


PREFACE 

A  course  in  business  arithmetic  should  train  the  pupil  to 
figure  correctly,  easily,  and  rapidly,  and  should  fit  him  to  solve 
the  problems  that  arise  in  the  ordinary  course  of  business.  To 
this  end  Modern  Commercial  Arithmetic  gives  a  brief  review 
of  the  fundamental  operations,  fractions  and  decimals^  intro- 
ducing short  practical  methods.  The  mechanical  part  of  arith- 
metic is  illustrated  and  explained  by  diagrams,  examples, 
operations,  and  notes.  The  intellectual  part  is  developed  in 
the  pupil's  mind  by  mental  problems,  questions,  and  state- 
ments. A  student  should  solve  a  problem  from  his  knowledge 
of  the  facts  or  conditions  of  the  problem  and  the  principles 
involved;  therefore,  rules  and  cases  are  superseded  by  develop- 
ment exercises  which  will  make  him  thoughtful  and  independent. 

In  the  business  office  problems  do  not  come  tabbed  with 
article  and  rule,  but  the  business  man  must  first  discover  the 
principle  that  is  involved  and  then  by  a  process  of  reasoning 
determine  the  result.  It  has  been  the  object  of  this  work  to 
present  the  problems  as  nearly  as  possible  as  they  are  presented 
in  the  business  office.  When  the  pupil  changes  from  the  school 
to  the  office  he  will  find  the  change  in  the  method  of  thought 
involved  as  slight  as  possible. 

The  student  in  school  has  no  time  to  waste  and  therefore 
this  work  contains  no  puzzles  or  catch  problems.  Subjects 
that  do  not  arise  in  ordinary  business  transactions  are  omitted. 

The  author's  aim  has  been  to  present  a  work  that  would 
give  the  pupil  such  instruction  as  he  needs,  and  to  set  it  forth 
in  the  manner  he  will  meet  it  in  the  business  office.  It  is 
hoped  and  believed  that  an  inspection  and  trial  of  the  work 
will  show  that  he  has  succeeded. 

210143 


CONTENTS 

PAGE 

NOTATION  AND  NUMERATION 7 

Arabic  Notation 7 

Roman  Notation 8 

ADDITION 10 

How  to  Make  Groups 10 

Cipher  Method 19 

Civil  Service  Method 21 

SUBTRACTION 23 

MULTIPLICATION 26 

Cross  Multiplication 29 

DIVISION 32 

THE  EQUATION 34 

CANCELLATION , 37 

FRACTIONS 40 

Decimal  Divisions  and  Decimal  Fractions 42 

How  to  Write  Decimals 43 

Addition  of  Decimals 45 

Subtraction  of  Decimals 46 

Division  of  Decimals 47 

Reduction  of  Fractions 49 

Addition  of  Common  Fractions 54 

Subtraction  of  Fractions 55 

Multiplication  of  Fractions 57 

Division  of  Fractions 59 

The  Three  Problems  of  Fractions. 61 

UNITED  STATES  MONEY 65 

OPERATIONS  WITH  ALIQUOT  PARTS.... 68 

PRICE,  COST,  AND  QUANTITY 71 

DENOMINATE  NUMBERS 76 

Linear  Measure 77 

Square  Measure 77 

4 


CONTENTS  5 

DENOMINATE  NUMBERS  PAGB 

Cubic  Measure 78 

Surveyors'  Measures 78 

Measures  of  Capacity 79 

Measures  of  Weight 79 

Troy  Weight 80 

Apothecaries'  Weight 80 

Measures  of  Time 80 

Measures  of  Angles 82 

Measures  of  Values 82 

Reduction  of  Denominate  Numbers...., 83 

Reduction  of  English  Money 87 

Fundamental  Operations 87 

Subtraction  of  Dates , 90 

Comparison  of  Weights  and  Measures 91 

Papers  and  Books 92 

Price,  Cost,  and  Mixed  Quantities 95 

PRACTICAL  MEASUREMENTS 102 

Land  Measurements 104 

Papering 115 

Carpeting 116 

Measurement  of  Solid  Figures 118 

Brick  and  Stone  Work 120 

Wood 121 

Lumber 122 

Practical  Rules  for  Dealers  in  Farm  Produce 125 

Square  Root 128 

PERCENTAGE .' 139 

PROFIT  AND  LOSS 150 

COMMISSION  AND  BROKERAGE 155 

TRADE  DISCOUNT 160 

MARKING  GOODS 164 

STORAGE 166 

INSURANCE 169 

Property  Insurance 169 

Personal  Insurance 172 

Table  of  Rates 175 

INTEREST 177 

Cancellation  Method 179 

1000-Day  Method 180 

Banker's  60-Day  Six  Per  Cent  Method 182 


6  CONTENTS 

INTEREST  PAGE 

Ordinary  Six  Per  Cent  Method , 185 

Periodic  Interest 190 

Compound  Interest 191 

Compound  Interest  Table 193 

Partial  Payments 201 

TRUE  DISCOUNT 207 

BANKING  BUSINESS 211 

Bank  Discount 211 

Bank  Deposits  and  Checks 214 

Collateral  Notes 218 

Domestic  Exchange 219 

The  Clearing  House 222 

Foreign  Exchange 227 

ACCOUNTS  AND  BILLS 229 

Bills— Trade  Discount 233 

Equation  of  Bills 235 

Equation  of  Accounts 241 

Accounts  Current 246 

Account  Sales 249 

PARTNERSHIP 251 

STOCKS  AND  BONDS 257 

TAXES 266 

MISCELLANEOUS  REVIEW  PROBLEMS...  ..  272 


MODERN  COMMERCIAL  ARITHMETIC 


NOTATION  AND  NUMERATION 

1.  The  writing  of  numbers  is  called  Notation. 

2.  The  reading  of  numbers  is  called  Numeration. 

3.  Numbers  may  be  written  in  three  ways:  5,  five,.V. 
The  first  method  was  used  by  the  Arabs,  and  it  is  called 

the  Arabic  system  of  notation. 

THE  ARABIC  SYSTEM 

4.  There  are  ten  figures  used  in  this  system.     Each  of  the 
following  figures  is  a  digit,  and  represents  a  number:  1,  2,  3, 
4,  5,  6,  7,  8,  9.     0  is  a  figure,  but  it  does  not  represent  a  num- 
ber.    It  is  used  with  other  figures  to  represent  numbers. 

In  counting,  units  are  grouped  into  units,  tens,  hundreds, 
thousands,  tens  of  thousands,  hundreds  of  thousands,  millions, 
etc.  10  of  one  group  make  1  of  the  next  larger  group.  Thus, 
10  units  make  1  ten,  10  tens  make  1  hundred,  10  hundreds 
make  1  thousand,  10  thousands  make  1  ten-thousand,  10  ten- 
thousands  make  1  hundred-thousand,  10  hundred-thousands 
make  1  million,  etc. 

The  number  1234567  contains  7  units,  6  tens,  5  hundreds, 
4  thousands,  3  tens  of  thousands,  2  hundreds  of  thousands,  and 

1  million.     It  may  be  described  as  7  units  of  the  first  order, 
6  of  the  second,  5  of  the  third,  4  of  the  fourth,  3  of  the  fifth, 

2  of  the  sixth,  and  1  of  the  seventh. 

5.  Principles. 

1.  Orders  of  units  increase  from  right  to  left  in  a  tenfold 
ratio. 

2.  Orders  of  units  decrease  from  left  to  right  in  a  tenfold 
ratio. 

7 


8  MODERN   COMMERCIAL   ARITHMETIC 

6.  In  reading  numbers,  three  figures  are  grouped  into  a 
period  and  read  as  follows : 

Millions,  Thousands,  Units 
203,  203,  203 

The  number  is  read:  203  million,  203  thousand,  203. 

EXERCISES 

7.  Eead:   3002,    42,005,    40,305,  400200,    40^204,    400Q20, 
402,030,   4003001,    4010,050,    50003002,    50030020,    50300200, 
300020070,  301201701,  110001010. 

Remark. — Numbers  above  hundreds  of  millions  are  seldom 
used  in  business.  When  used,  such  numbers  are  read  as  millions. 
Thus,  2467,845^27  is  read  2467  million,  845  thousand,  427. 

Write:  Twenty  thousand,  eighty.  One  hundred  thousand, 
forty-six.  Three  million,  thirty  thousand,  fifteen.  Two  hun- 
dred four  million,  eighteen  thousand,  one  hundred  fifty.  Two 
thousand  eighty-five  million,  seventy  thousand,  three.  Twenty 
million,  fourteen  thousand,  forty.  One  hundred  three  million, 
one  hundred  three.  One  thousand  four  million,  one  thousand, 
four.  One  thousand  five  million,  five  hundred  five  thousand, 
five  hundred  five. 

ROMAN   NOTATION 

8.  This  system  was  used  by  the  Komans. 

Letters  used:     I      V      X       L         C         D          M 
Values:  1       5       10       50       100       500       1000 

9.  Principles. 

1.  Eepeating  I,  X,  C,  or  M  repeats  its  value.     Thus,  III 
=  3,  XX  =  20,  CCC  =  300.    These  letters  are  not  repeated  more 
than  three  times,  although  we  find  IIII  on  clocks,  and  400  is 
sometimes  written  CCCC. 

2.  When  I  is  "before  V  or  X,  X  before  L  or  C,  C  before  D 
or  M,  the  values  of  the  letters  are  subtracted.     Thus,  IV  =  4, 
IX  =  9,  XL  =  40,  XC  =  90,  CD  =  400,  CM  =  900. 

3.  When  one  letter  is  placed  after  another  of  greater  value, 
their  values  are  added.     Thus,  VI  =  6,  XI  =  11,  LX  =  60,  CI 
=  101. 


DOTATION   AND   NUMERATION  9 

4.  A  dash  placed  over  a  letter  multiplies  its  value  by  1000. 
Thus  V  =  5000,  XI  =  11000,  LX  =  60000. 

10.  How  to  Write  Numbers. 

1.  Use  the  expressions  IV,  IX,  XL,  XO,  CD,  CM  as  one 
letter. 

2.  Write  the  letter,  or  expression,  whose  value  is  nearest 
that  of  the  required  number,  but  less  than  the  required  num- 
ber, and  add  letters  to  this  expression  until  the  required  number 
is  obtained. 

To  write  19,  first  write  10  (X),  then  add  9  (IX).  To  write 
28,  first  write  10  (X),  add  10  (X),  add  5  (V),  add  3  (III).  To 
write  49,  write  XL,  and  add  IX.  To  write  99,  write  50  (L), 
add  40  (XL),  add  9  (IX). 

11.  Write:  29,  34,  49,  51,  69,  89,  91,  219,  289,  391,  1047, 
1863,  1899,  1900,  20678,  4685,  3569,  56435,  4567,  1365,  3709. 

Eead:  XXXIX,  XCV,  XOIX,  CIX,  CXIX,  DOVI, 
DCCXXIX,  DCCCXL,  CMXIV,  MDCCXXVII,  MDCCCLXI, 
MCMXOIX. 


ADDITION 

12.  Addition  is  the  most  difficult  process  in  arithmetic,  for 
it  is  not  done  until  it  is  correctly  done.     When  the  columns  of 
numbers  added  are  long,  mistakes  are  likely  to  occur.     Care 
and  practice  are  necessary  to  enable  one  to  add  correctly  and 
with  a  reasonable  degree  of  rapidity.     Probably  the  first  test  or 
trial  an  employer  will  give  an  applicant  for  a  position  as  book- 
keeper will  be  to  add,  and  the  test  may  be  important.     Those 
who  add  well  generally  perform  the  other  operations  well.    It  is 
worth  while  to  learn  to  add  correctly  and  rapidly. 

13.  The  mental  process  in  adding  consists   in  grouping 
digits  of  the  same  order.     No  matter  how  many  the  numbers 
added  may  be,  the  whole  work  is  to  group  and  combine  digits. 
In  adding  by  any  method,  results  only  should  be  mentioned 
or  thought  of.    One  should  not  name,  even  mentally,  the  digits 
combined.     In  adding  the  digits  7,  2,  4,  6,  one  by  one,  think 
"9,  13,  19,"  not  "7  and  2  are  9,  9  and  4  are  13,  13  and  6 
are  19." 

Instead  of  adding  digits  one  by  one,  one  may  group  two  or 
more  digits  and  combine  the  groups.  Thus,  in  adding  4,  5, 
6,  2,  3,  7,  4,  6,  the  digits  may  be  combined  into  groups  of 
two  each.  Then  "17,  27,  37,"  thinking  of  results  only. 
Of  course,  one  may  think  of  the  groups  and  the  digits  in  the 
groups,  but  they  are  minor  subjects  of  thought.  The  attention 
should  be  on  the  results. 

HOW  TO  MAKE  GROUPS 

14.  Making  groups  and  combining  them  is  the  whole  of 
the  group  method.    In   combining  the  groups  it  is  important 
that  they  be  made  quickly  and  to  advantage.    It  is  easy  to  com- 
bine 10's  and  20's,  and  it  is  therefore  advantageous  to  make 
groups  of  10's  and  20's. 

10 


ADDITION  11 

Groups  of  two  digits  that  produce  10  • 

98765 
12345 

These  groups  should  be  recognized  at  sight.     Thus,  when 

7 

the  pupil  sees    ,  he  should  think  "10."     These  groups  should 
3 

be  so  well  known  that  the  pupil  may  give  his  whole  attention 
to  combining  the  groups. 

Groups  of  three  digits  that  produce  10 : 

11112223 
12342343 
87656  5  4  4 

Groups  of  three  digits  that  produce  20 : 

99998887 
98768767 
23454566 

All  possible  groups  of  two  digits  each.  There  are  only  45 
such  groups : 

111111111222222 
987654321234567 

223333333444444, 

893456789456789 

555556666777889 
567896789789899 

The  pupil  may  know  the  sum  of  each  of  these  groups, 
but  he  should  accustom  himself  to  think  of  the  sum  of  each 
group  instead  of  the  two  numbers  in  each  group.  He  should 
think  results  only,  and  should  be  thoroughly  drilled  on  these 
groups. 

Simplest  Group  Method 

15.  The  ordinary  pupil  has  learned  to  add  by  combining 
digits  one  by  one.  Thus,  in  adding  2,  5,  7,  3,  4,  2,  6,  3,  7,  2, 
he  thinks:  7,  14,  17,  21,  23,  29,  32,  39,  41. 

The  simplest  group   method   is   to  combine  two  or   more 


12  MODERN   COMMERCIAL   ARITHMETIC 

digits  whose  sum  is  10  or  less  than  10,  and  add  as  above*. 
Thus,  tl^e  pupil  in  adding  the  above  numbers  would  group  and 
think  as  follows,  the  numbers  in  parentheses  show  the  groups 
made:  (2,  5)  7,  (7,  3)  17,  (4,  2)  23,  (6,  3)  32,  (7,  2)  41. 

EXAMPLE. — Add  the  following  column  of  numbers,  making 
groups  of  10  or  less: 

435. 
274    7~; 

IQfr  EXPLANATION. — The'parentheses  show  the  groups  made. 

921  Begin  at  the  bottom  and  add  upward,  naming  results 
7g6  only.  (2,  5)  (6,  1)  14,  21,  (4,  5,)  30.  Write  0,  carry  3.  Add 
205  (3,  7)  10,  (8,  2)  20,  26,  (7,  3)  36.  Write  6,  carry  3.  Add 
(4,  2)  9, 16,  (9,  1),  26,  (4,  2)  32.  Write  32. 


3260 
EXAMPLE. — Add  the  following: 

6708 

4352 

1637  EXPLANATION. — Add   as   in   the   preceding   example. 

9452  (2,  6)  (3,  4)  15,  (2,  7)  24,  (2,  8)  34.    Write  4,  carry  3.     Add 

3614  3,  (5,  3)   11,  (7,  1)   19,  (5,  3)  27,  32.     Write  2,  carry  3.     3, 

2373  8,  16,  (3,  6)  25,  (4,  6),   35,  (3,  7)  45.     Write  5,   carry  4.     4, 

4836  (2,  4)  10,  (2,  3)  15,  (9,  1)  25,  (4,  6)  35.     Write  35. 

2552 


35524 

Straight  Grouping  and  Irregular  Grouping 

16.  Making  groups  of  digits  in  the  order  in  which  they  are 
written  may  be  called  straight  grouping.    Selecting  digits  out  of 
their  regular  order  to   make  groups   may  be   called  irregular 
grouping.    To  make  groups  equal  to  10  or  20,  it  may  be  neces- 
sary to  skip  about  in  the  column.    The  advantage  in  combining 
groups  of  10  and  20  justifies  such  irregular  grouping.    If  the 
digits  in  a  column  run  3,  0,  6,  7,  4,  we  may  group  3  and  7,  and  6 
and  4.    If  the  digits  run  8,  8,  7,  4,  we  may  group  8,  8,  and  4,  and 
leave  7  to  be  made  into  another  group  or  to  be  added  separately, 

PROBLEMS 

17.  Add  the  following  columns  of  numbers,  making  groups 
of  10  or  less: 


ADDITION 


13 


1.      &. 

3. 

4.     5. 

6. 

7. 

5843  25364 

465371 

386754  369625 

36825691 

46387625 

2671  72459 

245827 

538432  537167 

35718356 

18253751 

9326  72459 

274336 

276345  362841 

35624352 

26715436 

1473  57531 

524386 

534785  275146 

35625436 

63726354 

5845  14328 

295437 

369328  264375 

25634253 

63527152 

3264  46534 

624852 

574183  536271 

53462534 

26372453 

5728  73291 

735968 

263715  296345 

25635417 

35715487 

4532  52618 

243143 

497462  527164 

45278164 

53716482 

2674  45423 

538427 

513728  356278 

37452735 

37184527 

3426  28936 

253673 

354372  357281 

53672845 

25735427 

8. 

9. 

10. 

11. 

12. 

26748353 

25749574 

39615385 

25647154 

27845398 

17639052 

30816748 

25674926 

37185378 

26894536 

73620874 

20981632 

15674892 

37882567 

25037524 

10835627 

35718253 

71565735 

61782035 

26735526 

16738625 

35618536 

25637526 

35629816 

28019635 

19035276 

51673871 

26018635 

52673815 

27618763 

52176351 

56271463 

63728165 

73625437 

18674536 

93827362 

26173815 

37227384 

93026375 

27133926 

29637256 

34685647 

24674468 

34256709 

45136784 

25135487 

45789643 

23125376 

35867657 

98787656 

15463787 

23543476 

56984765 

25769804 

56875674 

25416748 

35984627 

35682536 

35987164 

37618835 

13. 

u* 

15. 

16. 

17. 

15367283 

15427685 

24537657 

43519687 

35239675 

27742625 

76865432 

76583251 

65763452 

76972541 

27531874 

76574532 

76457361 

45347648 

34135268 

77615524 

74563424 

76593425 

76583242 

76854325 

37106352 

76484323 

35246745 

76953420 

74693542 

35628163 

98063514 

63203516 

17035263 

87063521 

46245163 

90584615 

76845361 

25761536 

37825163 

27462738 

27093546 

16725830 

35627916 

25673541 

36547684 

70561825 

26174382 

25364534 

46874536 

25543423 

63572514 

27615437 

27645362 

25639653 

38762453 

18674523 

28764358 

26517094 

25763542 

29861542 

17625376 

35245142 

37617284 

25160939 

25167253 

17620935 

37825391 

25635427 

20198352 

35426155 

15269354 

26175243 

47654372 

25617542 

36812563 

36782546 

37652453 

37905615 

36873526 

26714526 

25634516 

53672534 

90635243 

63752635 

36254177 

24536426 

35745246 

35649182 

63725416 

73612803 

52719352 

26748234 

25436145 

26415536 

14 


MODERN   COMMERCIAL   ARITHMETIC 


18. 


19. 


21. 


43523543 

45315436 

165247 

253762 

375263 

67865434 

26794572 

167354 

352435 

635426 

32145673 

72326436 

156345 

635645 

435261 

87694351 

76945332 

896547 

457654 

365426 

37094532 

27840354 

265346 

256354 

486745 

7.6456324 

25653543 

254155 

244362 

256341 

96352743 

37615224 

175243 

524152 

263435 

25637184 

26185643 

864532 

367453 

365473 

37689452 

37614523 

163725 

367281 

354263 

27610934 

27615437 

908564 

367352 

532718 

28165437 

15426435 

256371 

453626 

376281 

28919735 

26514326 

187645 

291853 

109673 

36537462 

25637745 

902876 

267352 

536745 

38964532 

45673542 

873452 

145352 

536476 

25763415 

25346732 

253645 

547635 

348273 

53672543 

35426634 

273654 

351674 

536018 

25735462 

25639064 

534614 

425134 

234162 

82453142 

35261743 

256173 

356472 

291864 

24316423 

35241364 

156274 

852637 

254163 

24719342 

16354276 

526376 

256173 

253452 

84. 


25. 


27. 


367251 

256372 

356271 

253645 

109354 

376534 

254364 

256453 

256453 

755463 

534265 

547654 

345263 

264273 

453432 

276354 

243524 

756473 

356473 

253647 

345243 

254365 

345253 

764534 

251652 

371852 

634524 

271563 

254362 

253624 

735261 

278435 

253462 

156372 

357453 

356453 

482617 

251736 

251637 

253746 

352617 

356453 

926504 

251647 

352671 

356576 

453664 

345634 

354625 

356427 

946732 

534167 

352463 

245362 

834925 

261832 

256173 

352671 

764836 

874693 

768546 

675846 

764836 

536281 

648376 

534253 

356453 

457154 

376283 

473865 

381965 

409756 

381794 

361748 

356738 

389164 

361748 

657436 

358467 

876452 

571684 

356271 

254615 

345261 

357152 

356046 

647835 

280193 

355627 

861744 

357849 

609654 

351709 

356173 

254363 

524534 

645352 

764352 

267453 

352634 

ADDITION  15 

All  Possible  Groups  of  Three  Digits  Each 

18.  There  are  165  such  groups: 

1111111111111111111 
1111111112222222233 
1234567892345678934 

1111111111111111111 
3333344444455555666 
5678945678956789,6.  7-  8- 

1111111222222222222 
6777889222222223333 

9789899234567893456 

2222222222222222222 
3334444445555566667 
7894567895678967897 

2222233333333333333 
7788933333334444445 
8989934567894567895 

3333333333333344444 

5555666677788944444 
6789678978989945678 

4444444444444444555 

4555556666777889555 
9567896789789899567 

5555555555556666666 

5566667778896666777 
8967897898996789789 

6667777778889 
8897778898899 
8997898998999 

NOTE. — If  the  pupil  will  learn  to  think  the  sum  of  each  of  these 
groups  at  sight,  instead  of  adding  one  by  one,  or  two  by  two,  he  will 
be  able  to  add  three  digits  at  a  time.  He  may  omit  groups  whose  sum 
exceeds  20. 

Combining  Groups  between  10  and  20 

19.  It  is  easy  to  combine  groups  of  10's  and    20's.     It 
requires  practice   to   combine   rapidly   and   accurately  groups 
like  15,  17,  19.     In  combining  such  groups,  particular  atten- 


16 


MODERN   COMMERCIAL   ARITHMETIC 


tion  should  be  given  to  the  unit  figures,  for  mistakes  are  gener- 
ally made  in  combining  units,  not  in  combining  tens. 

All  the  combinations  (45)  that  can  be  made  with  numbers 
between  10  and  20  are  as  follows : 

11     11     11     11     11     11     11     11     11     12     12     12     12     12 

11  12     13     14     15     16     17     18     19     12     13     14     15     16 

12  12     12     13     13     13     13     13     13     13     14     14     14     14 

17  18     19     13     14     15     16     17     18     19     14     15     16     17 

14     14     15     15     15     15     15     16     16     16     16     17     17     17 

18  19     15     16     17     18     19     16     17     18     19     17     18     19 


18 
18 


18 
19 


19 
19 


The  unit  figures  in  these  groups  are  the  same  as  those  in 
the  45  combinations  of  the  nine  digits.  The  sum  of  the  tens 
is  2  in  each  group.  If  the  sum  of  the  units  in  any  group  is  10 
or  more,  the  tens  in  that  group  will  be  increased  by  1.  Think 
what  the  unit  figure  will  be.  Then  the  tens  figure  will  be 
either  2  or  3.  If  the  combinations  of  the  digits  have  been 
learned,  the  combinations  of  these  numbers  will  soon  be  mas- 
tered. Combining  16  and  19  is  the  same  as  combining  6  and 
9,  and  adding  2  tens  to  the  sum.  Combining  any  two  numbers 
between  10  and  20  is  the  same  as  combining  their  unit  figures, 
and  increasing  the  sum  by  2  tens. 

Device  for  Drill  Work 

2O.  Let  the  teacher  draw  on  the  board  a  diagram  like  the 
following :  In  the  space  between  the  two  rings  are  all  the  numbers 
between  10  and  20.  In  the  center  may 
be  placed,  successively,  each  of  the  num- 
bers between  10  and  20.  The  pupil 
should  be  required  to  combine  the  num- 
ber in  the  center  with  each  number 
between  the  rings,  naming  only  the 
sum  of  the  numbers.  The  pupil  should 
begin  at  o.ie  point  and  go  around  the 
ring.  Thus  he  may  begin  at  12,  and 
say:  25,  27,  30,  etc.  This  device  will  give  thorough  'and  rapid 


ADDITION  17 

drill,  and  the  pupil  may  profitably  use  it  outside  of  the  reci 
tation. 

All  Combinations  of  Numbers  between  10  and  20  with  all 
Numbers  between  10  and  100 

21.  If  the  pupil  can  make  these  combinations  readily,  he 
will  be  in  possession  of  the  "lightning  method." 

If  the  pupil  has  learned  the  combinations  under  Art.  19, 
he  can  readily  learn  the  combinations  under  this  article.  The 
wheel  for  drill  work  under  Art.  20  may  be  used  to  develop  all 
the  possible  combinations  here.  With  the  numbers  between  10 
and  20  in  the  wheel,  and  the  number  13  in  the  center,  as  shown 
in  the  diagram,  the  pupil  may  make  81  combinations.  Thus, 

13 

beginning  with      ,  which  he  can  see  on  the  wheel,  he  may  con- 
tinue mentally, 

13     13     13     13     13     13     13     13 

22     32     42     52     62     72     82     92 

13 
Then  he  may  take      ,  the  next  combination  on  the  wheel,  and 

combine 

13     13     13     13 
24     34     44     54 

etc.     Next  he  may  combine 

13     13     13     13 

17     27     37     47 

and  so  on.     He  may  use  each  number  between  10  and  20  in 
the  center. 

There  are  no  more  combinations  of  units  under  this  article 
than  there  are  under  Art.  19.  The  only  difference  is  in  the 
tens. 

PROBLEMS 

22.  Solve  the  problems  under     Art.    17,  making  groups 
of  numbers  from  10  to  20  inclusive. 

Also  add  the  following  columns. 

NOTE.— Some  teachers  may  prefer  to  omit  this  exercise  now,  and 
teach  the  pupil  to  add  by  the  cipher  method  or  by  the  method  of  re- 
jecting tens. 


18 


MODERN    COMMERCIAL    ARITHMETIC 


1. 

g. 

3. 

4. 

5. 

6. 

7. 

746092 

356189 

849756 

357925 

672109 

261752 

251673 

615427 

256352 

256381 

987536 

267154 

256371 

377163 

635867 

263451 

253645 

386728 

904625 

109725 

376281 

251673 

376184 

456098 

378194 

476386 

837625 

156253 

906498 

378294 

783902 

389173 

371839 

274681 

378294 

274891 

356745 

278357 

287467 

173823 

490879 

387164 

547993 

371846 

275637 

190896 

389523 

779174 

265784 

537683 

453789 

809251 

437892 

709261 

345672 

456728 

245681 

907896 

475829 

356281 

167493 

267356 

908957 

534tfi7 

264357 

785536 

671526 

390895 

378456 

267453 

908576 

378164 

467584 

467582 

367153 

178098 

190758 

256173 

381745  ] 

189047 

356174 

637456 

190467 

378594 

352635 

467189 

356453 

578264 

390183 

354671 

267184 

345671 

278590 

675987 

461736 

254367 

356174 

256738 

354672 

567438 

546781 

689053 

563748 

253672 

356478 

534672 

356271 

386478 

467590 

409873 

536728 

356278 

156253 

•  273884 

534721 

254671 

356713 

356183 

356472 

256173 

356174 

276453 

371809 

309814 

456173 

356172 

309735 

253781 

367184 

276153 

908153 

456153 

460981 

376154 

124563 

908945 

356278 

267493 

251674 

748367 

8. 

9. 

10. 

11. 

12. 

13. 

14. 

554367 

356904 

378904 

356076 

365243 

377815 

251436 

635736 

356253 

346891 

380965 

356253 

368256 

356189 

536715 

253671 

356872 

268467 

901645 

276489 

256378 

356187 

256184 

356209 

378915 

256109 

350987 

536173 

356187 

356274 

356278 

256173 

256374 

366453 

356274 

904687 

378987 

367187 

789762 

356274 

378190 

378167 

859045 

356287 

153617 

354613 

674657 

356184 

678098 

352464 

456374 

465745 

341745 

389178 

467589 

671523 

526354 

657890 

351647 

456374 

467563 

152463 

351672 

256153 

356456 

789153 

467819 

378918 

678193 

609871 

261873 

678163 

254167 

409871 

564073 

378109 

367194 

360192 

108391 

357184 

356273 

371835 

674839 

789463 

908758 

478567 

675876 

678354 

617356 

256173 

371835 

785094 

367184 

367184 

153723 

478194 

367855 

361738 

901746 

352617 

361846 

453152 

768970 

345241 

768970 

152435 

678706 

132453 

670078 

451324 

670789 

453314 

352415 

676097 

678796 

345241 

253425 

678709 

679687 

352415 

674533 

463718 

894675 

678969 

352453 

678698 

256104 

453253 

609687 

908968 

675446 

467364 

354672 

674352 

352673 

356278 

162543 

908718 

674098 

361014 

ADDITION 


19 


IB. 


16. 


17. 


18. 


19. 


367183 

356280 

467587 

467584 

567483 

467384 

374837 

389106 

671908 

367184 

361893 

267134 

235243 

676987 

253617 

453671 

360985 

473645 

342515 

678678 

567483 

901235 

367183 

253671 

356183 

268493 

256109 

356173 

906879 

467354 

368193 

367281 

467384 

453674 

281947 

960687 

453627 

352415 

657869 

906879 

567483 

352633 

109273 

456378 

907685 

758495 

356475 

617382 

354609 

470194 

367495 

467382 

638485 

133749 

351848 

546473 

905736 

351635 

451736 

251674 

467583 

101886 

461735 

905681 

253471 

456183 

901857 

567685 

567685 

678509 

891025 

675847 

467584 

467584 

567485 

391046 

908679 

906870 

567006 

564732 

152453 

674536 

514235 

671884 

155367 

251453 

617352 

184761 

352785 

906875 

647382 

905768 

574857 

567485 

678968 

906879 

678596 

132453 

102947 

647283 

467384 

362718 

253647 

895047 

850495 

102847 

564738 

291837 

647859 

905748 

356173 

785686 

605674 

172959 

637152 

675448 

152673 

718938 

188965 

536718 

354678 

996574 

471836 

768006 

675869 

567281 

387596 

162839 

452637 

152435 

261745 

352674 

786960 

678957 

456374 

568676 

787967 

857465 

860978 

564735 

The  Cipher  Method 

23.  By  this  method  the  student  makes  groups  of  10's  and 
20's,  and  combines  them  with  the  other  digits  in  groups  or  one 
by  one.  By  practice  in  irregular  grouping,  the  student  can 
put  many  of  the  digits  into  groups  of  10  or  20. 

The  following  columns  show  how  such  groups  may  be  made: 


53 


20  MODERN    COMMERCIAL   ARITHMETIC 

PROBLEMS 

24.  Look  through  the  columns  of  figures  under  Articles 
17  and  22,  and  make   groups  of  10's  and  20's.     Skip  about 
if  necessary,  but  do  not  try  to  put  all  the  digits  into  such 
groups. 

NOTE.  —  The  teacher  should  assign  some  of  the  problems  under 
Articles  17  and  22,  to  be  added  by  the  cipher  method. 

Method  of  Rejecting  10's 

25.  By  this   method  the   student  rejects  the   10's  (does 
not  hold  them   in  memory),  but  retains  them  on   a  piece  of 
paper  or  on  the  fingers.    The  mind  is  thus  relieved  from  keep- 
ing account  of  the  10's,  and  addition  becomes  an  easy  operation. 
The  student  adds,  one  by  one  or  by  groups,  until  he  has  from 
10  to  20,  rejects  10,  begins  again  with  what  he  has  left  and  adds 
until  he  has  from  10  to  20,  rejects  10,  and  so  on. 

EXAMPLE.  —  Add  the  following  column  of  numbers,  rejecting 
10's: 

EXPLANATION.  —  Begin  at  the  bottom.    Add  6,  2  and  8  ; 
having  more  than  10,  drop  10  and  begin  again  with  the  6 
left  (for  every  10  dropped,  makes  a  mark  on  a  slip  of  paper). 
""^       Add  6  and  7;  having  more  than   10,  drop  10  and  begin 
•~*       again;  add  3  and  9,  drop  10  and  begin  over;  add  2,  2,  4, 
and  6,  drop  10  and  begin  over;   add  4  and  6,  drop  10;  add 


4,  2,  and  4,  drop  10.  There  are  no  units  left.  Write  0  in 
'  ~*  units'  place.  5  tens  have  been  dropped.  Add  the  second 
column,  including  the  5  tens  dropped  from  the  first. 
Add  5,  3,  and  5,  drop  10;  add  3,  6,  and  3,  drop  10;  add 
2,  4,  8,  drop  10;  add  4,  3,  7,  drop  10;  add  4,  3,  8,  drop  10; 
write  ^the  5  left,  and  carry  the  5  dropped.  Add  the  third 
column,  including  the  5  dropped  from  the  second.  Add  5, 


7250       8)  dr°P  10;  add  3»  7>  dr°P  10;  add  4>  5>  6>  dr°P  10;  add  5)  7' 
drop  10;  add  2,  9,  drop  10;  add  1,  8,  7,  drop  10;  add  6,  6, 

drop  10 ;  write  the  2  left,  also  write  the  7  dropped. 

NOTE.— Hold  the  units  clearly  in  mind,  but  merely  notice  the  tens. 
The  tens  are  to  be  dropped  from  memory,  and  are  to  be  recorded  by 
some  device.  When  adding  7  and  9,  think  6  and  record  1  ten  as 
being  dropped.  If  the  next  number  to  be  added  is  8,  think  4  and 
record  1  ten.  Give  close  attention  to  the  units,  give  just  enough  at- 
tention to  the  tens  to  record  them. 


ADDITION  21 

Device  for  Recording  10's 

26.  The  following  cut  shows  how  the  10's  may  be  recorded. 
Number  the  joints  of  the  thumb, 

beginning  at  the  end,  5,  10,  15;  the 
joints  of  the  first  finger,  1,  6,  11; 
the  second  finger,  2,  7,  12;  the  third 
finger,  3,  8,  13;  and  the  fourth 
finger,  4,  9,  14. 

To  record  1  ten,  place  the  thumb  on  the  joint  of  the  little 
fingermarked  1.  In  like  manner,  2  tens,  3  tens,  and  4  tens 
may  be  recorded  on  the  other  fingers.  To  record  5  tens, 
straighten  the  thumb.  To  record  6  tens,  place  the  thumb  on 
the  second  joint  of  the  little  finger.  In  like  manner,  7  tens, 
8  tens,  and  9  tens  may  be  recorded  on  the  other  fingers.  To 
record  10  tens,  straighten  the  thumb.  And  so  on.  By  a  little 
practice,  the  pupil  will  be  able  to  record  the  tens  on  his  hand 
and  know  when  he  is  through  with  a  column  just  how  many 
tens  have  been  dropped.  If  the  count  ends  when  his  thumb 
is  straightened,  he  must  know,  of  course,  whether  it  has  been 
straightened  once,  twice,  or  three*  times.  If  any  column  con- 
tains more  than  15  tens,  the  student  may  repeat  the  count  on 
his  hand. 

Civil  Service  Method  of  Recording  Partial  Sums 

27.  If  the  sum  of  each  column  added  be  written  in  full, 
instead  of  writing  but  one  figure,  the  accountant  can  leave  his 
work  after  adding  part  of  the  number  of  columns  and  resume 
it  without  re-adding  any  of  the  columns.     The  addition  of  any 
column  may  be  verified  without  re-adding  the  other  columns  to 
find  the  figure  carried. 

The  following  illustrates  the  method : 

4628 

7394  25              Tne  sums  °f  the  columns  are  25,  30,  28,  26, 

5462  30         an(*  ^ney  are  written  under  one  another,  each 

6856  28           succeeding  number  one  place  to  the  left.     The 

4785  26              partial  sums  are  then  added  and  the  result  placed 

—       under  the  numbers  added. 

29125 


MODERN    COMMERCIAL   ARITHMETIC 

EXERCISES 

28.  Look  through  the  columns  under  Articles  17  and  22, 
and  combine  the  digits,  dropping  the  tens  and  thinking  of  the 
units  only.     Do  not  record  the  tens,  but  drop  them. 

Add  the  columns  under  Articles  17  and  22  by  repeating  the 
above  exercise,  keeping  on  the  hand  a  record  of  the  tens  dropped 
and  writing  the  proper  figure  under  each  column. 

Horizontal  Addition 

29.  Sometimes   numbers  that  are  to  be  added   are  found 
written  in   horizontal  lines.     They  can   be  added  without  re- 
writing them  in  vertical  columns.    In  adding  horizontally,  from 
right  to  left  or  from  left  to  right,  care  must  be  taken  to  com- 
bine only  like  orders  of  units. 

PROBLEMS 
SO.  Add  the  following : 

1.  45,  34,  67,  35,  98,  56,  74,  37,  25,  74,  34,  64. 

2.  123,  435,  609,  524,  274,  315,  376,  903,  457. 

3.  260,  789,  635,  256,  235,  170,  585,  370,  245. 

4.  1245,  3465,  9075,  1260,  4561,  2351,  6754,  4532. 

5.  2745,  706,  486,  3450,  235,  5687,  250,  1274,  378. 

6.  652,  3476,  6789,  376,  4523,  8097,  560,  4563,  276. 

7.  476,  6453,  254,  8609,  560,  3124,  3654,  450,  231. 

8.  3500,  3540,  350,  3456,  873,  2578,  2154,  687,  3542. 

9.  5476,  9050,  576,  3542,  1456,  684,  9085,  541,  355. 

10.  35672,  5609,  90504,  526,  500,  8050,  45763,  375. 

11.  3540,  6750,  4535,  548,  46876,  78045,  362,  4752. 

12.  45,  687,  50943,  475,  9967,  4500,  450,  35460. 

13.  4536,  567,  9075,  32165,  45,  768,  75,  35025,  268,  4575. 

14.  550,  6735,  98,  675,  558,  75,  35450,  265,  4235. 

15.  3750,  790,  89,  563,  4576,  256,  950,  5425,  635. 

16.  4576,  9056,  75,  356,  87,  2457,  675,  9050,  350. 

17.  5490,  5467,  580,  25,  69,  599,  4563,  2875,  654. 

18.  4678,  6780,  47,  387,  5674,  3265,  745,  87,  4765. 

19.  367,  90,  9835,  453,  69,  2543,  657,  45,  76255. 

20.  54376,  9004,  5476,  899,  654,  37459,  362,  7623. 


SUBTRACTION 

Subtraction  by  Addition 

31.  EXAMPLES. 

786     minuend 
243     subtrahend 

543     remainder 

243        +       543        =      786 
subtrahend  -f-  remainder  =  minuend 

243  +  ?  =  786 

To  find  the  remainder,  find  a  number  which  added  to  the 
subtrahend  will  produce  the  minuend.  The  best  way  to  find 
that  number  is  to  add  to  the  subtrahend,  digit  by  digit,  until 
the  minuend  is  produced.  Solving  the  example  at  the  top  of 
this  page,  one  would  say,  beginning  at  the  right  hand,  3  (sub- 
trahend) and  3  (write  it  in  the  remainder)  are  6  (minuend).  4 
(sub.)  and  4  (write  in  rem.)  are  8  (min.)  2  (sub.)  and  5  (write 
in  rem.)  are  7  (min.) 

EXAMPLE. — From  968  take  425. 

OPERATION 

968  EXPLANATION. — 5  (sub.)  and  3  (rem.)  are  8  (min.)    2 

425        (sub.)  and  4  (rem.)  are  6  (min.).     4  (sub.)  and  5  (rem.)  are 

9  (min.). 

543 

EXAMPLE.— From  7023  take  4326. 

EXPLANATION.— 6  (sub.)  and  7  (rem.)  are  13  (which 
7023  gives  tne  figure  in  the  minuend).  Carry  1.  2  (sub.)  and  1 
4.39R  (carried)  and  9  (rem.)  are  12  (min.).  4  (sub.)  and  1  (car- 

ried)  and  2  (rem.)  are  7(min.)    This  process  is  called  sub- 

2697       traction  by  addition.     It  is  easy,  and  is  productive  of  the 
highest  degree  of  accuracy  and  rapidity. 
23 


24  MODERN    COMMERCIAL    ARITHMETIC 

PROBLEMS 

1.  4670-2463  =  ?  9.  507433-285362  =  ? 

2.  8609-3726  =  ?  10.  429728-136475  =  ? 

3.  2432-1716  =  ?  11.  16078435-    1356428  =  ? 

4.  2586-1654  =  ?  12.  24736842-21687584  =  ? 

5.  130765-124587  =  ?  IS.  42687903-26875486  =  ? 

6.  728062-257465  =  ?  14.  87065435-84736247  =  ? 

7.  709354  -  467152  =  ?  15.  80035463  -  78200456  =  ? 

8.  370816-281029  =  ?  16.  56190364-49015246  =  ? 

32.  Two  or  more  subtrahends : 

EXAMPLE.— From  86798  take  21342,  26584,  and  22765. 

EXPLANATION. — The  operation  is  similar  to  the  process 
°f  "Subtraction  *>y  Addition."    Instead  of  adding  the 
remainder  to  one  subtrahend  we  add  it  to  three  subtra- 
2134,       hends.     Thus,  5,  8,   2  (sub.)  and  3  (rem.)  are  18  (min.). 
6,  4,  4  (sub.)  and  1  (carried)  and  4  (rem.)  are  19  (min.). 
%"<65      7,  5,  3  (sub.)  and  1  (carried)  and  1  (rem.)  are  17  (min.).    2, 
16143      6>  *  (sub.)  and  1  (carried)  and  6  (rem.) are  16  (min.).     2, 
2,  2  (sub.)  and  1  (carried)  and  1  (rem.)  are  8  (min.). 

33.  This  method  is  often  convenient  in  finding  the  balance 
of  an  account.     The  above  problem  may  be  written  and  solved 
as  follows : 

(  21342 

subtrahends  \  26548 

(  22765 

remainder     16143 

minuend     86798 
Prom  the  following  statement  find  the  net  gain : 

GAINS  LOSSES 

$4260  $324 

1273  1673 

1647  246 

365  113 

426  Net  gain     

$7971  $7971 

NOTE. — Add  up  the  gains.  Place  the  sum  under  the  losses.  Add 
losses,  and  write  for  the  net  gain  such  digits  as  added  to  the  losses  will 
produce  $7971,  and  balance  the  account. 


SUBTRACTION  25 

34.  PROBLEMS 

1.  From  9467  take  2135,  1682,  1478,  and  2692. 

2.  From  12784  take  6253,  3786,  and  2057. 

3.  From  28650  take  10652,  8549,  3267,  and  1026. 

4.  From  156709  take  24680,  13793,  16745,  and  24863. 

5.  From  84907  take  16243,  14786,  9352,  and  27054. 

6.  From  246532  take  73855,  12736,  and  96854. 

7.  From  42584  take  12653,  11964,  and  13867. 

8.  From  89756  take  21684,  14793,  16248,  and  13728. 

9.  From  126087  take  43568,  13752,  28537,  and  21864. 

10.  From  254375  take  62873,  94852,  14695,  and  17586. 

11.  From  48692  take  12071,  9825,  4687  and  14650. 

12.  From  &4508.75  take  $1328.14,  $924.68,  $156.90,  $437.15 
and  $260. 54. 

13.  From  $39575.40  take  $4681.25,  $11060.50,  $16245.30 
and  $716.90. 

14.  From  $12825.70  take  $625.25,  $513.42,  $765.34  and 
$1486.76. 

15.  From  $28746.80  take  $9458.28,  $7134.35,  $863.47, 
$6479.58,  $143.92. 

16.  From  $137248. 75  take  $41980.40,  $3714.24,  $9652.18, 
$4£?3.62  and  $31967.86. 

17.  From  $125876.85  take  $1463.25,  $4563.54,  $3287.43 
and  $458.35. 

18.  From  $981.44  take  $135.72,  $368.27,  $94.25,  $126.36, 
$72.83,  $43.28. 

19.  From  $3574.50  take  $1247.31,  $719.85,  $64.27,  $435.63 
and  $246. 33. 

20.  From  $42867.25  take  $19763.45,  $1564.22,  $867.14, 
$938.53  and  $6537.48. 


MULTIPLICATION 

35.  The  product  is  composed  of  the  same  kind  of  units  as  is 
the  multiplicand,  and  the  multiplier  is  an  abstract  number. 
But  as  the  product  of  two  numbers  is  the  same  whichever  factor 
is  used  as  a  multiplier,  either  factor  may  be  regarded  as   the 
multiplier. 

EXAMPLE. 

246     multiplicand 
3     multiplier 

738     product 

36.  Know  the  multiplication  table  up  to  10  x  10. 

Multiplication  Table 

123456789   10 

2  4   6   8  10  12  14  16  18   20 

• 

3  6   9  12  15  18  21  24  27   30 

4  8  12  16  20  24  28  32  36   40 

5  10  15  20  25  30  35  40  45  50 

6  12  18  24  30  36  42  48  54  60 

7  14  21  28  35  42  49  56  63  70 

8  16  24  32  40  48  56  64  72  80 

9  18  27  36  45  54  63  72  81  90 

10  20  30  40  50  60  70  80  90  100 
26 


MULTIPLICATION  27 

Numbers  between  10  and  20 

37.  EXAMPLE.— Multiply  12  by  13. 

EXPLANATION.—  2  x  3  =  6.     The  product  of  the 

OPERATION  units  is  6,  which  write.      The  product  of  tens  by 

12x13  =  156       units  is  10  X  2  +  10  X  3  =  50,  or  5  tens,  which  write. 

The  product  of  the  tens  is  1  (hundred),  which  write. 

NOTE.— The  product  of  any  two  numbers  between  10  and  20  is 
composed  of  three  parts :  the  product  of  the  units,  the  product  of  the 
units  by  the  tens,  and  the  product  of  the  tens.  The  product  of  the 
units  by  the  tens,  in  tens,  is  always  the  sum  of  the  units.  The  product 
of  the  tens  is  always  1  (hundred).  Therefore,  take  the  product  of  the 
units  for  the  units,  the  sum  of  the  units  for  the  tens,  and  1  for  the 
hundreds.  If  the  product  or  the  sum  of  the  units  is  more  than  9,  carry 
as  usual. 

EXAMPLE.— Multiply  14  by  15. 

OPERATION  EXPLANATION.— 5  X  4  =  20.  Write  0,  and  carry  2. 

14x15  =  210       5  +  4  =  9.     9  +  2  (carried)  =  11.    Write   1,  carry  1. 
1  (hundred)  +  1  (carried)  =  2,  which  write. 

PROBLEMS 

Find  the  product  of : 

1.  13  x  14.       7.  14  x  17.      18.  19  x  19. 

2.  14  x  15.       8.  15  x  18.      14.  14  x  18. 
8.  13  x  15.       9.  16  x  19.      15.  17  x  15. 

4.  15x16.  10.  17x18.  16:  17x14. 

5.  13  x  17.  11.  15  x  19.  17.  12  x  18. 

6.  13  x  19.  12.  16  x  18.  18.   18  x  19. 

NOTE. — The  pupil  should  learn  to  perform  these  operations  men- 
tally, and  the  teacher  may  assign  other  problems  of  the  same  kind. 

Multiplying  by  10,  100,  1000,  Etc. 

38.  If  one  cipher  (0)  be  annexed  to  a. number.,  by  what 
is  the  number  multiplied?     If  two  ciphers  (00)  be  annexed  to 
a  number,  by  what  is  the  number  multiplied?     If  three  ciphers 
(000)  be  annexed? 


28  MODERN    COMMERCIAL    ARITHMETIC 

MENTAL  PROBLEMS 

Find  the  product  of : 

1.  87  x  100.  8.  872  x  10000.       5.  368  x  10000. 

2.  605  x  1000.       4.   9651  x  100.          6.  7524  x  1000. 

Multiplying  Numbers  with  Ciphers  at  the  Eight  Hand 

39.  EXAMPLE.— Multiply  860  by  2400. 

OPERATION  EXPLANATION.  —Multiply  the  digits, 

86  x  24  =  2064  then  to   the  product  annex  as  many 

2064  x  10  x  100  =  2064000.     ciphers  as  are  found  at  the  right  of  both 

factors. 

PROBLEMS 
Find  the  product  of: 

1.  27  x  1300.          8.   5200  x  137000.     5.   1240  x  1400. 

2.  680  x  12400.     4.  2600  x  18000.       6.  3500  x  16000. 

Multiplying  by  a  Number  Near  100,  1000,  etc. 

40.  EXAMPLE.— Multiply  246  by  99. 

EXPLANATION. — Multiply  246  by  100  by 

OPERATION  annexing  two  ciphers.  99  is  1  less  than  100. 

246  x  100  =  24600  Therefore,  multiply  246  by  99  by  subtract- 

24600  -  246  =  24354      ing  once  246  from  24600.    Or,    annex  two 
ciphers  and  subtract  246. 

EXAMPLE.— Multiply  425  by  997. 
OPERATION 

425000  EXPLANATION. —  Annex  three   ciphers  and  sub- 

425  x  3  =  1275    tract  3  times  425. 
423725 

EXAMPLE.— Multiply  425  by  1003. 
OPERATION 

425000  EXPLANATION.— Annex  three  ciphers  and  add  3 

425  x  3  =  1275    times  425. 
426275 


MULTIPLICATION  29 

PROBLEMS 

NOTE.— Do  not  write  the  multiplier,  and  write  the  multiplicand  but 
once. 

Find  the  product  of : 

1.  875  x  99.  5.  3075  x  995.  8.  2073  x  105. 

0.  6032  x  998.  6.     732  x  102.  9.  358  x  1003. 

8.  587  x  97.  7.     864  x  1004.  10.  2561  x  106. 

4.  6802x996. 


CROSS  MULTIPLICATION 

When  Each  Factor  Contains  Two  Figures 

41.  EXAMPLE.— Multiply  21  by  23. 

Steps  in  the  operation: 
1.  Units  by  Units  21  \  3x1  =  3  Units. 

23' 
OPERATION 

21  x  23  =  483    2-  Tens  by  Units  21    2x3  +  2x1  =  8  Tens. 

/^ 
23 

3.  Tens  by  Tens  /21  2x2  =  4  Hundreds. 

V23 

EXPLANATION.— In  multiplying  units  and  tens  by  units  and  tens, 
there  are  three  steps:  finding  the  product  of  units  by  units,  the  product 
of  tens  by  units  and  the  product  of  tens  by  tens.  The  product  of  the 
units  is  3,  which  write  for  the  units  of  the  complete  product.  The 
product  of  the  tens  by  the  units  is  8  tens  (3X2  +  2X1),  which  write 
for  the  tens  of  the  complete  product.  The  product  of  the  tens  by  the 
tens  is  4  hundreds,  which  write  for  the  hundreds  of  the  complete 
product.  If  any  partial  product  be  more  than  9,  carry  as  usual. 

EXAMPLE. — Multiply  48  by  35. 

EXPLANATION. —  First    step,   5X8  =  40,    units. 
OPERATION         Write  0,  carry  4.  Second  step,  5x4  +  3x8  +  4  (car- 
48  x  35  =  1680    ried)  =  48  tens.    Write  8,  carry  4.     Third  step,  3x4 
+  4  (carried)  =  16  hundreds,  which  write. 


30  MODERN   COMMERCIAL   ARITHMETIC 

PROBLEMS 

NOTE. — Write  the  factors  in  a  horizontal  line  and  perform  the 
operations  mentally. 

Find  the  product  of: 

1.  42x34.  6.  74x53.  11.  37x46.  16.  37x89. 

2.  53  x  27.  7.   67  x  58.  12.  48  x  53.  17.  46  x  74. 

3.  62  x  43.  8.  95  x  36.  13.  75  x  26.  18.  38  x  92. 

4.  73  x  28.  9.  46  x  58.  14.  83  x  47.  19.  79  x  62. 

5.  68  x  94.          10.  29  x  35.  15.  64  x  93.  20.   88  x  69. 

When  the  Multiplicand  Contains  More  Than  Two  Figures 

42.  EXAMPLE.— Multiply  235  by  24. 

EXPLANATION. — There  is  one  more  step  in  the 
OPERATION  operation  than  there  are  figures  in  the  multiplicand. 

235  x  24  =  5640     Omitting  the  carrying  figures,  the  steps  are  as  fol- 
lows: 

235\  235 

1.  )    5  X  4  =  20  units.        S.   X      2x4  +  3x2  =  14  hundreds. 
24'  24 

2.  X      3X4  +  5X2  =  22  tens.      4-  (  '  '    2x2  =  4  thousands. 
Write  the  proper  figures  and  carry  as  usual. 

EXAMPLE.— Multiply  4376  by  57. 

NOTE. — The  steps  in  the  operation  may  be  illustrated  thus: 


4376\       4376      4736      4376       /4376 
57/        57       57       57        \57 


EXAMPLE.— Multiply  43765  by  57. 

NOTE.— The  steps  in  the  operation  may  be  illustrated  thus: 

43765\  43765  43765  43765  43765  /4376S 

57/  57  57  5^  57  \57 

PROBLEMS 

NOTE. — Write  the  factors  in  a  horizontal  line  and  perform  the 
operations  mentally.    This  method  is  convenient  in  extending  bills. 

1.  234  x  23.         3.    567  x  38.         5.  4306  x  42.         7.  1236  x  63. 

2.  426  x  34.         4.  1214  x  35.         6.  7308  x  54.         8.  4253  x  76. 


MULTIPLICATION  31 


9.    1684x57. 
10,    2173x65. 

11.    4287  x  29. 
12.  64261x36.^ 

18.  23784  x  75. 
14.  40265  x  84. 
•  15.  25738  x  73. 
16.    6381  x  76. 

mt~    17.    9017x39.     s# 
#v  IS.  65182x82.   <-- 
\fjfa4  19.  52781  x  87.  *  /  ft  I  *' 
;  >f     £0.     6910x94. 

Multiplying  by  Two  Figures  One  of  Which  is  1 

43.  This  is  usually  given  as  a  special  method,  but  in  its 
simplest  form  it  is  cross  multiplication. 

PROBLEMS 
Find  the  product  of : 

1.  236x13.      5.  8316x31.        9.     237x19.  18.  1378x12. 

2.  472x14.      6.  7026x18.      10.  1384x91.  14.  7813x16. 
8.  1238x17.       7.  1682x41.      11.  2765x71.  15.  836x61. 
4.  2036x21.      8.  2361x51.      12.  1683x15.  16.  7825x81. 

To  Multiply  by  11 

44.  Although   usually  given   as  a   special  method  this  is 
simply  cross  multiplication. 

PROBLEMS 

Find  the  product  of : 

1.  18x11.         5.  315x11.  9.  356x11.  18.  1362x11. 

2.  26x11.         6.  246x11.  10.   943x11.  14.  2480x11. 
8.  135x11.         7.  719x11.  11.  257x11.  15.  7156x11. 
-f     76x11.         5.263x11.  10.645x11.  1(5.3062x11. 


DIVISION 

45.      Illustration  of  Terms  and  Proof  of  Division 

40-5  8 

dividend  -  divisor     =  quotient 

5x8         =40 
divisor  x  quotient  =  dividend 

40       +       8  5 

dividend  -  quotient  =  divisor 

128  -  5  =  25  and  3  remainder,  written  f ,  3  to  be  divided  by  5. 
divisor  x  quotient  -f  remainder  (if  any)  =  dividend 

Hence  to  prove  division,  multiply  together  the  divisor  and 
quotient  and  to  the  product  add  the  remainder.  If  the  result 
equals  the  dividend  the  work  is  correct. 

46.  Principles. 

24-4  =  6         48-4  =  12         12-4  =  3 

1.  Multiplying  the  dividend  multiplies  the  quotient;  divid- 
ing the  dividend  divides  the  quotient. 

24-4  =  6         24-8  =  3  24-2  =  12 

2.  Multiplying  the  divisor  divides  the  quotient;    dividing 
the  divisor  multiplies  the  quotient. 

24-4  =  6         48+8  =  6          12-2  =  6 

3.  Multiplying  or  dividing  both  dividend  and  divisor  by  the 
same  number  does  not  change  the  value  of  the  quotient. 

Short  Long  Division 

47.  This  is  the  ordinary  method  of  long  division  shortened 
by  introducing  the  "subtraction  by  addition"  method  and  by 
multiplying  and  subtracting  at  the  same  time. 


DIVISION 


33 


EXAMPLE.— Divide  721098  by  291. 

EXPLANATION. —The  first  figure  of  tho  quo- 
tient is  2.  Multiply  the  divisor  by  2  and  subtract 
the  product  from  721  as  follows:  2X1  =  2  and 
9  (which  write  for  the  remainder)  are  11. 
2x9  =  18-and  1  (carried)  are  19  and  3  (write  in 
remainder)  are  22.  2x2  =  4  and  2  (carried)  are 
6  and  1  (write  in  remainder)  are  7.  Bring  down 
the  next  figure  of  the  dividend,  making  the 
remainder  1390.  Multiply  291  by  4  and  subtract.  4x1  =  4  and  6  are 
10.  4  X  9  =  36  and  1  are  37  and  2  are  39.  4X2  =  8  and  3  are  11  and 
2  are  13.  Bring  down  the  next  figure  of  the  dividend,  making  the 
remainder  2269.  Multiply  291  by  7  and  subtract.  7X1  =  7  and  2  are  9. 
7  X  9  =  63  and  3  are  66.  7  X  2  =  14  and  6  are  20  and  2  are  22.  Bring 
down  the  8.  Multiply  291  by  8  and  subtract. 


OPERATION 
291)721098(2478 
1390 
2269 
2328 
0000 


PROBLEMS 


Find  the  quotient  of: 


1. 


5. 
6. 
7. 
8. 
9. 
10. 


11445  + 

10664- 

30128  + 

11312644- 

1691823- 

313194106  - 

1243414986  -  58327. 

302418  -      954. 

205683-      629. 

2151090-    4185. 


35. 

24. 

56. 

7856. 

357. 

7153. 


11. 


IS. 

14. 
15. 
16. 
17. 
18. 
19. 
20. 


1085. 

317. 

654. 

423. 

2136. 

4874. 

2576. 

- 16843. 


1091510 - 
135676- 
6220848  * 
4687238- 
7098643  -' 
9364725  - 
537654-*- 
1068432- 
2764379-    4268. 
876543  -      769. 
48.  Dividing  by  10,  100,  1000,  etc. 

Principle. — Cutting  off  one  figure  from  the  right  of  the  divi- 
dend divides  it  by  10,  cutting  off  two  figures  divides  it  by  100, 
cutting  off  three  figures  divides  it  by  1000,  etc.  The  part  of 
the  dividend  cut  off  is  the  remainder. 

PROBLEMS 
Find  the  quotient  of: 

1.  46800-      100.  '.;  6.  420070-        1000. 

2.  73000-    1000.  7.       53781936-    100000. 

3.  2860-      100.  8.     800167829-      10000. 

4.  796800-10000.  9.     670197356-1000000. 


5.  63875-  1000. 


10.  5179036527  + 1000000. 


THE  EQUATION 

49.  The  sign  of  equality  (=)  between  two  equal  numbers 
or  expressions  forms  an  Equation. 

7  +  2=9.     4x5  +  3  =  6x3  +  5.     Cost  of   25  cows  =  cost  of 
100  sheep. 

minuend  -  subtrahend  =  remainder 
dividend  -*-         divisor  =  quotient 

Axioms 

50.  Truths  so  simple  that  they  do  not  admit  of  proof  are 
called  Axioms. 

1.  Things  equal  to  the  same  thing  are  equal  to  each  other. 

If  $600  =  cost  of  25  cows,  and 

$600  =  cost  of  100  sheep, 
then  cost  of  25  cows  =  cost  of  100  sheep. 

2.  If  equals  are  added  to  equals  the  sums  are  equal. 

If  cost  of  25  cows  =  cost  of  100  sheep, 
then  cost  of  25  cows  +$100  =  cost  of  100  sheep  +  $100. 
If  A  =  B,  then  A  +  C  =  B  +  C. 


3.  If  equals  are  subtracted  from  equals  the  remainders  are 
equal. 

If  cost  of  25  cows  =  cost  of  100  sheep, 
then  cost  of  25  cows  -$100  =  cost  of  100  sheep  -$100. 
If  A=B,  then  A-0  =  B-C. 

4.  If  equals  are  multiplied  by  equals  the  products  are  equal. 

If  cost  of  25  cows  =  cost  of  100  sheep, 
then  cost  of  100  cows  =  cost  of  400  sheep. 
If  A  =  B,  then  A  x  C  =  B  x  C. 
34 


THE    EQUATION  35 

5.  If  equals  are  divided  by  equals  the  quotients  are  equal. 

If  cost  of  25  cows  =  cost  of  100  sheep, 
then  cost  of  5  cows  =  cost  of  20  sheep. 
If  A  =  B,  then  A  +  C  =  B  +  C. 

51.  The  process  of  changing  a  number  from  one  side  of 
an  equation  to  the  other  is  called  transposition. 

(1)  A-10  =  B 

Add  10  to  both  sides  (members)  of  the  equation  (Axiom  2,)  and 
(2)  A-10  +  10  =  B  +  10,  or  A  =  B  +  10 

In  the  first  equation,  10  is  in  the  first  member ;  in  the  sec- 
ond equation,  10  is  in  the  second  member.  The  sign  of  10  in 
the  first  equation  is  — ,  in  the  second  +.  10  has  been  changed 
from  one  member  of  the  equation  to  the  other,  and  its  sign  has 
been  changed  from  —  to  +. 

(3)  A  +  10  =  B 

Subtract  10  from  both  members  of  the  equation,  and 

(4)  A  =  B-10 

10  has  been  changed  from  one  member  of  the  equation  to  the 
other,  and  its  sign  has  been  changed  from  +  to  — . 

52.  Principle. — A  number  may  be  transposed  from  one 
member  of  an  equation  to  the  other  by  changing  its  sign  from 
+  to  - ,  or  from  —  to  + . 

Solution  of  the  Equation 

53.  If  in  any  equation  there  is  a  term  whose  value  is  not 
given,  as  A  =  3  +  7,  finding  the  value  of  that  term  is  called  solv- 
ing the  equation. 

NOTE. — It  is  a  common  error  to  take  the  signs  of  addition,  subtrac- 
tion, multiplication  and  division  in  the  order  in  which  they  come.  The 
signs  of  multiplication  and  division  have  the  preference  over  the  signs 
of  addition  and  subtraction,  and  the  operations  indicated  by  the 
former  are  to  be  performed  before  those  indicated  by  the  signs  of  the 
latter,  thus: 

2  +  9  X  6  =  56,  not  66 


36  MODERN    COMMERCIAL   ARITHMETIC 

In  every  equation  the  plus  or  the  minus  sign  must  be  understood  to 
affect  the  result  of  the  whole  operation  indicated  between  it  and  the 
next  plus  or  minus,  or  between  it  and  the  close  of  the  expression. 

If  a  problem  is  stated  in  the  form  of  an  equation,  solving 
the  equation  is  solving  the  problem. 

PROBLEMS 
54.  Solve  the  following  equations: 

1.  Cost  of  horse  =  $100  4- $6  x  10.  (Find  the  cost  of  the  horse.) 

2.  A  =  65  4-32 -7. 

3.  Cost  of  2  cows  =  $18  +  $3  x  10:     (Find  cost  of  one  cow.) 

4.  2  A  =  18  +  3  x  10.     (Find  value  of  A.) 

5.  Cost  of  stove  +  $10  =  $40.     (Find  cost  of  stove.) 

6.  Cost  of  horse  -  $15  =  $60. 

7.  Value  of  3  horses  =  $210.     (Find  value  of  a  horse.) 

8.  Value  of  3  horses  -  $15  =  i 

9.  Value  of  3  horses  4- $10  =  1 

10.  Value  of  8  cows  =  $1920  +  6. 

11.  Value  of  5  sheep  4- $12  =  $42. 

12.  A 4-6x8  =  504- 23. 

18.  Dividend  =  12  x  360  4-  40. 

14.  Subtrahend  - 165  =  586. 

15.  How  many  cows  at  $25  per  head  =  $600? 


CANCELLATION 

55.  Cancel  means  to  mark  out.     Cancellation  is  division  by 
marking  out  or  crossing  out  factors.     The  dividend  consists  of 
two  factors :   the  divisor  and  quotient.     If  one  of  these  factors 
be  marked  out,  the  other  factor  will  remain.     The  divisor  itself 
maybe  separated  into  factors.     When  both  divisor  and  dividend 
contain  like   factors,    such   factors  may  be  cancelled  without 
changing  the  value  of  the  quotient. 

Cancellation  is  the  process  of  rejecting  common  factors  from 
both  dividend  and  divisor.     (See  Principle  3,  Art.  46.) 

56.  EXAMPLE. 

Divide  6  x  8  x  12  x  15  x  20  by  2  x  3  x  4  x  5  x  30. 

Instead  of  dividing  the  product  of  the  first  set  of  factors  by  the 
product  of  the  second  set,  we  may  cancel  the  common  factors 
and  then  divide  if  a  divisor  remains  uncancelled. 

EXPLANATION.—  Write 
OPERATION 

the  factors  of  the  dividend 

0  $  ,  12  10  ^0  above  a  horizontal  line  and 

—  =  48  the  factors  of  the  divisor 

*  49  30^  below.  Then  reject  equal 

factors  from  both  dividend 

and  divisor.  The  factors  2  and  3  in  the  divisor  cancel  6  (2X3)  in 
the  dividend.  4  and  5  in  the  divisor  cancel  20  (4  X  5)  in  the  divi- 
dend. 15  in  the  dividend  cancels  15  (one  of  the  factors  of  30)  in  the 
divisor,  leaving  the  factor  2  instead  of  30  in  the  divisor.  This  2  can- 
cels 2  (one  of  the  factors  of  8)  in  the  dividend,  leaving  4  instead  of 
8  in  the  dividend.  In  the  dividend  there  remain  the  factors  4  and  12, 
which  produce  48,  the  required  quotient. 

Exact  Divisors 

57.  1.  2  is  an  exact  divisor  of  any  even  number. 

2.  3  is  an  exact  divisor  of  any  number  the  sum  of  whose 
digits  is  divisible  by  3. 

37 


38  MODERN    COMMERCIAL    ARITHMETIC 

3.  5  is  an  exact  divisor  of  any  number  ending  with  5  or  0. 

4.  9  is  an  exact  divisor  of  any  number  the  sum  of  whose 
digits  is  divisible  by  9. 

5.  No  even  number  is  an  exact  divisor  of  an  odd  number. 

PROBLEMS 

58.  Cancel  when  you  can,  multiply  when  you  must. 
Divide : 

1.  45  x  16  x  60  x  27  by  15  x  8  x  12  x  9  x  4. 

2.  96  x  128  x  72  x  64  by  16  x  48  x  27. 

8.  33  x  57  x  72  x  216  by  19  x  11  x  8  x  27  x  16. 

4.  872  x  365  x  496  by  654  x  175  x  428. 

5.  384  x  495  x  350  by  352  x  330  x  210. 

6.  345  x  432  x  120  by  210  x  360  x  216. 

7.  882  x  225  x  168  by  556  x  315  x  112. 

8.  616  x  512  x  420  by  560  x  448  x  315. 

9.  A  man  exchanged  24  loads  of  wheat,  each  weighing  2480 
pounds,  worth  80  cents  per  bushel  of  60  pounds,  for  59  barrels 
of  sugar,  each  weighing  420  pounds.    What  was  the  price  of  the 
sugar  per  pound? 

10.  A  farmer    sold  18  loads  of   hay,  each  weighing  2860 
pounds,  at  $21  per  ton  of  2000  pounds.     He  received  in  pay- 
ment 8  loads  of  phosphate,  each  load  containing  12  bags,  and 
each  bag  240  pounds.     What  was  the  price  of  the  phosphate 
per  100  pounds? 

11.  How  many  city  lots,  each  containing  21   square  rods, 
and  valued  at  $8  per  square  rod,  are  equal  in  value  to  15  fields, 
each  containing  1120  square  rods,  valued  at  $32  per  acre  of  160 
square  rods? 

12.  How  many  pieces  of  cloth,  each  containing  126  yards, 
valued  at  16  cents  per  yard,  are  equal  in  value  to  35  pieces  of 
cloth,  each  containing  288  yards,  valued  at  14  cents  per  yard? 

18.  If  18  barrels  of  beef,  each  containing  200  pounds,  are 
worth  $288,  what  will  75  pounds  cost  at  the  same  rate? 

14.  If  52  men  can  dig  a  ditch  in  42  days,  working  9  hours 
a  day,  how  many  days  will  be  required  by  24  men  to  do  the 
same  work,  if  they  work  7  hours  per  day? 


CANCELLATION  39 

15.  How  many  boxes  of  tobacco,  each  weighing  42  pounds, 
valued  at  90  cents  per  pound,  are  equivalent  to  80  boxes  of 
tobacco,   each  weighing   149   pounds,  valued  at  81  cents   per 
pound? 

16.  Divide  120  x  540  x  695  by  380  x  175. 

17.  250  x  25  x  84  x  21  =  365  x  80  x  32  x  ? 

18.  The  factors  of  the  dividend  are  940,  760,  145,  and  724. 
The  factors  of  the  divisor  are  190,  724,   235,  and  180.     Find 
the  quotient. 

19.  A  bicyclist  rode  8  miles  an  hour  for  18  days  of  10  hours 
each  and  walked  back  at  the  rate  of  3  miles  per  hour.     How 
many  days  did  it  take  Jrim  to  get  back,  if  he  walked  12  hours 
a  day? 

20.  How  many  days'  work,  of  10  hours  each,  at  15  cents 
per  hour,  will  be  required  to  pay  for  a  pile  of  wood  48  feet  long, 
4  feet  wide,  and  9  feet  high,  at  $4.50  per  cord? 

21.  How  many  boards  16  feet  long  and  12  inches  wide,  at 
$24  per  thousand,  must  be  given  in  exchange  for  160  scantling 
2  inches  by  4  inches  and  18  feet  long,  at  $14  per  thousand? 

22.  How  many  bricks  2  inches  by  4  inches  by  8  inches  will 
be  required  to  lay  a  wall  14  feet  long,  6  feet  high,  and  1^-  feet 
thick? 

23.  How  many  village  lots  6  rods  by  8  rods,  worth  $6  per 
square  rod,  are  equal  in  value  to  a  farm  80  rods  by  90  rods,  at 
$96  per  acre? 

24.  At  $26  per  thousand,  how  many  sticks  4  inches  by  6 
inches  by  14  feet  are  equal  in  value  to  130  boards  18  feet  long 
and  12  inches  wide,  at  $45  per  thousand? 

25.  How  many  days,  of  9  hours  each,  must  a  man  work,  at 
18  cents  per  hour,  to  pay  for  a  fot  120  feet  by  165  feet,  at 
$8  per  square  rod? 


FRACTIONS 

59.  If  a  whole  is  divided  into  two  or  more  equal  parts,  the 
parts  are  called  fractions  of  the  whole.     One  of  the  parts  is  a 
fraction.     Several  of  the  parts  are  a  fraction. 

Division  is  the  process  of  separating  a  unit  or  a  number  into 
equal  parts. 

One-seventh  of  1,  one-ninth  of  1,  one-tenth  of  1,  are  frac- 
tions, for  they  are  each  equal  parts  of  a  unit. 

One-seventh  of  4,  one-ninth  of  4,  one-tenth  of  4,  are  frac- 
tions, for  they  are  each  equal  parts  of  a  number. 

A  fraction  is  one  or  more  of  the  equal  parts  of  a  unit,  or 
one  of  the  equal  parts  of  a  number. 

f  shows  2  of  the  3  equal  parts  into  which  a  unit  is  divided, 
or  it  shows  that  2  is  divided  into  3  equal  parts. 

A  fraction  is  division  indicated  by  the  sign  /.  1-^-2  and  \ 
are  the  same  in  value,  f  \  and  27  -f-  36  are  the  same  in  value. 

60.  In  a  fraction,  the  dividend  (number  above  the  line)  is 
called  the  Numerator.     It  enumerates,  or  tells,  how  many  of 
the  equal  parts  of  a  unit  are  included  in  the  fraction,  or  it 
shows  what  number  has  been  divided  into  equal  parts.     The 
fraction  f  shows  3  of  the  5  equal  parts  into  which  the  unit  is 
divided,  or  it  shows  that  3  is  divided  into  5  equal  parts. 

61.  The  divisor  (number   below   the  line)    is   called   the 
Denominator.     It  names  the  parts  into  which  a  unit  or  a  num- 
ber is  divided.     If  the  denominator  is  4,  it  shows  that  a  unit 
or  a  number  is  divided  into  fourths. 

62.  A  fraction  indicates  division.     The  value  of  a  fraction 
is  therefore  the  quotient  of  the  division  indicated.     A  fraction 
is  a  quotient.     The  numerator  and  denominator  are  called  the 
terms  of  a  fraction.     The  dividend  and  divisor  are  called  tb« 
terms  of  a  division. 

40 


FRACTIONS  41 

Comparing  fractions  with  division,  the  numerator  is  the 
dividend,  the  denominator  is  the  divisor,  and  the  fraction  is  the 
quotient. 

Principles  of  Division 

63.  1.  Multiplying  the  dividend  multiplies  the  quotient, 
dividing  the  dividend  divides  the  quotient. 

2.  Multiplying  the  divisor  divides  the  quotient,  dividing  the 
divisor  multiplies  the  quotient. 

3.  Multiplying  or   dividing  both  dividend  and   divisor  by 
the  same  number  does  not  change  the  value  of  the  quotient. 

Principles  of  Fractions 

64.  1.  Multiplying  the  numerator  multiplies  the  fraction, 
dividing  the  numerator  divides  the  fraction. 

2.  Multiplying  the  denominator  divides  the  fraction,  divid- 
ing the  denominator  multiplies  the  fraction. 

3.  Multiplying  or  dividing  both  numerator  and  denominator 
by  the  same  number  does  not  change  the  value  of  the  fraction. 

Terms 

65.  A  Proper  Fraction  is  one  whose  numerator  is  less  than 
its  denominator;  as,  f,  £,  |. 

An  Improper  Fraction  is  one  whose  numerator  equals  or 
exceeds  its  denominator;  as,  f,  f,  y. 

A  Mixed  Number  is  one  expressed  by  an  integer  and  a 
fraction ;  as,  4f ,  read  four  and  three-fifths. 

A  Complex  Fraction  is  one  which  has  a  fraction  in  one  or 

s      5      92 

both  of  its  terms ;  as,  -|>  ^ ?  -—• 
fv    *t     C 

A  Compound  Fraction  consists  of  two  or  more  single  frac- 
tions joined  together  by  the  word  of;  as,  f  of  f  of  f . 

PROBLEMS 
Write  the  following  in  the  form  of  fractions : 

1.  One-half  over  six-fifths. 

2.  Four  over  eight-seventeenths. 


42  MODERN    COMMERCIAL    ARITHMETIC 

3.  Mne-tenths  of  eight  and  two-thirds. 

4.  Seven-ninths  of  four-sevenths. 

5.  Six  and  seven-eighths  over  nine  and  three-fourths. 

DECIMAL   DIVISIONS   AND   DECIMAL  FRACTIONS 

66.  If  1000  is  divided  into  10  equal  parts,  what  is  one  of 
the  parts  called?  Perform  the  operation  by  pointing  off  one 
figure. 

If  100  is  divided  into  10  equal  parts,  what  is  one  of  the 
parts  called?  Perform  the  operation  by  pointing  off  one  figure. 

If  10  is  divided  into  10  equal  parts,  what  is  one  of  the  parts 
called?  Perform  the  operation  by  pointing  off  one  figure. 

If  1  is  divided  into  10  equal  parts,  what  is  one  of  the  parts 
called?  Perform  the  operation  by  pointing  off  one  figure. 

If  .1  is  divided  into  10  equal  parts,  what  is  one  of  the  parts 
called?  Point  off  one  figure  as  before.  Put  a  cipher  between 
the  period  (decimal  point)  and  the  one  to  show  that  onevplace 
more  has  been  pointed  off. 

If  .01  be  divided  into  10  equal  parts,  what  is  one  of  the 
parts  called?  Point  off  as  before.  Insert  another  cipher. 

If  .001  is  divided  into  10  equal  parts,  what  is  one  of  the 
parts  called?  Point  off  as  before,  and  insert  another  cipher. 

The  divisions  of  a  number  into  tenths,  hundredths,  thou- 
sandths, etc.,  are  Decimal  Divisions,  or  Decimal  Fractions. 

PROBLEMS 

Divide  by  pointing  off  (insert  ciphers  when  necessary)  and 
read  the  quotients : 

1.  1+  10.  10.       10-1000000. 

2.  1  +          100.  11.       25  +          100. 
ft  I-*-        1000.  12.       25  +        1000. 

4.  3  +  10.  IS.       25-*-      10000. 

5.  3-    100.        14.   25+  100000. 
£.3  +   1000.        15.   25  +  1000000. 

7.  1+   10000.        16.  136+   1000. 

8.  1+  100000.        17.  136+   10000. 

9.  1  +  1000000.        18.  1378  +  1000000. 


DECIMAL   DIVISIONS   AND    DECIMAL   FRACTIONS  43 

67.  By  what  must  1  be  divided  to  produce  .01?  Read  .01. 
By  what  must  1  be  divided  to  produce  .001?  Read  .001.  By 
what  must  1  be  divided  to  produce  .0001?  Read  .0001.  Read 
.0007,  .00001,  .00005,  .000001,  .000006,  .000021,  .00055. 


DECIMAL  SCALE  OF  ARABIC  NOTATION 


1 


1  1  I  1  1  „  .  i  1  I  1  1  1 
I  1  I J  i:  1 1  I  v  I  !  !  I  I 

7654321234567 

68.  Repeat  the  scale  from  millions  to  millionths,  from  mil- 
lionths  to  millions. 

The  decimal  point  is  always  before  tenths.  Repeat  the  scale 
from  the  decimal  point  each  way. 

The  name,  or  denomination,  of  a  decimal  is  that  of  its  right- 
hand  order  of  units.  Thus,  .0001  is  one  ten 'thousandth. 


How  to  Write  Decimals 

69.  According  to  our  system  of  writing  we  begin  at  the  left 
and  write  toward  the  right.  This  is  the  case  with  script  and 
also  with  figures.  For  the  sake  of  economy  of  time  and  to  be 
consistent,  pupils  should  learn  to  write  decimals  in  the  same 
manner  and  according  to  the  following  rules: 

1st.  Fix  the  decimal  point. 

2d.  Think  of  the  number  of  places  required  to  make  a  frac- 
tion of  the  given  denominator. 

3d.  Think  of  the  number  of  places  given  in  the  numerator. 

4th.  Beginning  at  the  right  of  the  decimal  point,  write  as 
many  ciphers  as  are  required  to  make  the  number  of  places 
given  -equal  to  the  number  required,  and  follow  these  by  the 
numerator,  or  the  figures  given. 


44  MODERN    COMMERCIAL   ARITHMETIC 

7O.  Write  decimally: 

1.  3  thousandths. 
1st.  Fix  the  point. 

3d.  It  requires  three  places  to  make  thousandths. 

3d.   One  place  is  given. 

4th.  At  the  right  of  the  point  write  two  ciphers,  then  the  3. 

2.  135  millionths. 

3.  3  millionths ;  345  hundred-thousandths ;  45  millionths. 

4.  23456  millionths;  356  hundred-millionths. 

5.  Eighteen  ten-thousandths.     Twenty-seven  hundred-thou- 
sandths.    One  hundred  sixty-five  millionths.     Thirty-four  ten- 
thousandths.   One  hundred  eight  hundred-thousandths.    Eighty 
millionths. 

6.  Twenty-five  and  twenty-six  thousandths. 

NOTE.— The  word  and  is  used  to  connect  a  whole  number  and  a 
decimal.  This  expression  is  written  25.026. 

7.  One  hundred  and  seventy-eight  ten-thousandths.  •  One 
hundred  seventy -eight  ten-thousandths. 

8.  Four  hundred  sixty-three  and  four  hundred  sixty-three 
ten-millionths.  Four  hundred  and  forty-seven  ten-thousandths. 
Four  hundred  forty-seven  ten-thousandths. 

9.  Six   hundred-thousandths.     Six    hundred   thousandths. 
Three   hundred    ten  thousandths.     Three  hundred  ten-thou- 
sandths. 

10.  Three  hundred  eighty  thousand  and  thirteen  thousand 
four  hundred  ninety- six  hundred-thousandths. 

EXERCISES  IN  NUMERATION 

71.  The  numerator  of  a  decimal  is  the  number  expressed 
by  the  figures  of  the  decimal.  It  is  the  number  divided  into 
tenths,  hundredths,  thousandths,  etc.  The  denominator  of  a 
decimal  is  indicated  by  the  decimal  point  and  by  the  number  of 
figures  following  the  decimal  point.  The  decimal  point  stands 
for  1 ;  each  figure  in  the  decimal  stands  for  a  cipher  following 
that  1.  The  denominator,  if  expressed,  would  be  1  with  as  many 
ciphers  annexed  as  there  are  figures  at  the  right  of  the  decimal 
point. 


FRACTIONS  45 

EXERCISES 
Read  the  following: 

1.  .00125. 

NOTE. — There  are  two  parts  to  the  operation:  reading  the  numer- 
ator and  reading  the  denominator.  Read  the  numerator  as  if  it  were 
a  whole  number.  To  read  the  denominator,  begin  at  the  decimal  point 
and  numerate  toward  the  right,  thus :  tenths,  hundredths,  thousandths, 
ten-thousandths,  hundred-thousandths.  The  decimal  is  one  hundred 
twenty-five  hundred-thousandths. 

2.  .000367,  .1709,  .00231,  .100236,   .00002,  .000367. 

3.  .07,  .0028,  .6400,  .056843,  .0086003,  .00008. 

4.  18.34. 

NOTE. — This  is  read  18  and  34  hundredths.  In  reading  mixed 
numbers,  it  is  necessary  to  connect  the  integral  and  fractional  parts 
by  and. 

5.  127.0034,  13.2006,  1780.0073,  146000.146. 

6.  400.04,  10000.010,   10.010,  200.003,   .203. 

7.  .00800654,  3800.0076,  56.7003804,  4800.7063. 

8.  3674583.000437,  2687.015008,  3268.007583. 

9.  1200.0012,  3984.05307,  100300.00301,  37.0000045. 
10.  256784370.4600736,  4300.56032,  140000.00007554. 

72.  Compare  .3,  .30,  .300,  .3000  as  to  value. 
Compare  .3,  .03,  .003,  .0003  as  to  value. 

Principles:  —  1.  Annexing  ciphers  to  a  decimal  does  not 
change  its  value. 

2.  Inserting  a  cipher  between  the  decimal  point  and  the 
decimal  figures  divides  the  decimal  by  10. 

3.  Decimal  orders  of  units  increase  and  decrease  in  value  the 
same  as  do  orders  of  units  in  whole  numbers. 

Addition  of  Decimals 

73.  Principle. — Only  like  orders  of  units  can  be  added. 
EXAMPLE.— Add  .265,  13.7,  and  1.3787. 

OPERATION  EXPLANATION. — Write  the  numbers  so  that  the 

.265  decimal  points  fall  in  a  vertical  line,  and  units  of 

13.7  the  same  order  will  stand  in  the  same  column.     Add 

1.2787  as  in  integers,  and  put  the  decimal  point  in  the  sum 

1*>  34-37  directly  under  the  points  in  the  numbers  added. 


46  MODERN    COMMERCIAL   ARITHMETIC 

PROBLEMS 

Find  the  sum  of : 

1.  .14,  1.268,  3.72,  4.682,  15.79. 

2.  31.06,  128.374,  175.009,  38.063,  53.034. 

3.  504.017,  3.86,  7.128,  130.065,  14.586. 

4.  .0038,  100.16,  9.054,  .69786,  1687.98745. 

5.  432.867,  576.09,  78.659,  9.85,  15.462. 

6.  .3286,  14.567,  284.007,  1275.49,  36.5976. 

7.  12,  14.825,  .7364,  129,  16.004,  157.3697. 

8.  47.25,  6.0078,  174.6,  9.678,  23.00159. 

Subtraction  of  Decimals 

74.  Principle.  — Only  like  orders  of  units  can  be  subtracted. 
EXAMPLE.— From  48.73  take  25.6274. 

OPERATION  EXPLANATION.— Write  the  numbers  as  in  addi- 

48.73  tion.     Consider  ciphers  as  annexed  to  the  minuend, 

25.6274  and  subtract.  Put  the  decimal  point  in  the  remainder 

23. 1026  directly  under  the  points  in  the  numbers  subtracted. 

PROBLEMS 
Find  the  remainder  of: 

1.  .832 -.126.  5.  179.86-138.0583. 

2.  15.06-7.2584.  6.  4085.75-927.6485. 
S.  460.85-53.265.  7.  928.6482-25.7595. 
4.  246.7385-39.74.  8.  16843.7652-483.28. 

Multiplication  of  Decimals 

75.  Tens  x  tens  =  hundreds.     10  x  10  =  100. 
Tens  x  hundreds  =  thousands.     10  x  100  =  1000. 
Hundreds  x  hundreds  =  ten-thousands.     100  x  100  =  10000. 
Hundreds  x  thousands  =  hundred-thousands.      100  x  1000  = 

100000. 

Tenths  x  tenths  =  hundredths.     .1  x  .1  =  .01. 

Tenths  x  hundredths  =  thousandths.     .1  x  .01  =  .001. 

Hundredths  x  hundredths  =  ten -thousandths.  .01  x  .01  = 
.0001. 

Hundredths  x  thousandths  =  hundred-thousandths.  .01  x 
.001  =  .00001. 


FRACTIONS  47 

Principle. — The  product  contains  as  many  decimal  places  as 
there  are  decimal  places  in  the  factors. 
EXAMPLE.— Multiply  1.256  by  .32. 

OPERATION 

-^  25g  EXPLANATION.— Multiply  as  in  whole  numbers.  Point 

32  off  as  many  decimal  places  in  the  product  as  there  are 

decimal  places  in  both  factors. 

2512  NOTE.— If  there  are  not  enough  figures  in  the  product 

3768  to  point  off,  prefix  ciphers  to  the  product.    Thus,  .2  X  .04 

."40192      =-°08- 

PROBLEMS 

Find  the  product  of: 

1.  .83x1.4.  11.  1000x10. 

2.  1.75x.23.  12.  .001x10. 

8.  . 272  x. 081.  18.  1.001  x  .0001. 

4.  .064x1.5.  14.  . 0001  x. 001 

5.  . 0053  x. 029.  15.  10.001  x  .00001. 

6.  2.0038  x  .00016.  16.  1000  x  .001. 

7.  4.062  x. 0037.  17.  10001.0001xl.001. 

8.  .0155x1.8.  18.  10000.0001x10000. 

9.  27.08  x. 125.  19.  5005.005x5000. 

10.  523  x. 00017.  20.  500.0005x5000.000005. 

Division  of  Decimals 

76.  .05  x  .005  =  .00025.  Hence,  .00025  +  .05  =  .005,  and 
.00025  +  .005  =  .05. 

Principle. — The  quotient  contains  as  many  decimal  places  as 
the  number  of  decimal  places  in  the  dividend  exceed  those  in 
the  divisor. 

EXAMPLE  1.— Divide  .00036  by  .004. 

EXPLANATION. — Divide  as  in  whole  numbers. 
Point  off  in  the  quotient  as  many  decimal  places 
as  the  number  of  decimal  places  in  the  dividend 
.004).00036(.09  exceed  those  in  the  divisor.  5  —  3  =  2.  Prefix 
one  cipher  to  the  quotient,  and  point  off  two 
places. 

SUGGESTIONS.  —1.  If  the  quotient  does  not  contain  enough  figures 
to  point  off,  prefix  ciphers. 


48  MODERN   COMMERCIAL   ARITHMETIC 

2.  Before  dividing,  make  the  number  of  decimal  places  in  the  divi- 
dend at  least  equal  to  the  number  of  places  in  the  divisor,  by  annexing 
ciphers  to  the  dividend. 

3.  When  all  the  figures  of  the  dividend  have  been  used  and  there  is 
a  remainder,  annex  ciphers  to  the  dividend  and  continue  the  division. 

4.  Ordinarily  it  is  not  necessary  to  extend  the  division  to  more 
than  four  decimal  figures  in  the  quotient. 

PROBLEMS 
Find  the  quotient  of: 

1.  68.125-25.  6.  .0357-51000. 

2.  16.025 -*•  .045.  7.  625-*- .0025. 

5.  52.848-09.  8.  20-75. 

4.  75 -.00125.  9.  723.68-143. 

5.  .0065-125.  10.  2.652-17. 

EXAMPLE  2.— Divide  638.25  by  300. 

OPERATION 

300)6.3825  EXPLANATION.— Cut  off  the  two  ciphers  in  the 

divisor  and  point  off  two  places  in  the  dividend,  begin- 

2.1275  ning  at  tne  decimal  point.  Then  divide  6.3825  by  3. 

11.  675-50000.  15.  865-124000000. 

12.  428.6-200.  16.  97.281-900. 
IS.  .373-4000.  ^17.  57800-8000000. 
U.  1728-1200©.  18.  .6307-700. 

Ten  problems  are  given  in  each  of  the  following  groups. 
The  object  is  to  drill  the  pupil  in  pointing  off. 

State  the  quotient  in  the  form  of  a  decimal  fraction  in  each 
of  the  following  problems : 

19.                                20.  21. 

2-2.                           1-2.  4-25. 

2 -.02.                        1-200.  400 -.25. 

20-2.                          .1-.2.  .4-2500. 

2 -.2.                          .01-20.  .004 -.0025. 

20 -.002.                    .0001 -.2.  .4 -.000025. 

.2-2.                          100 -.002.  4000 -.000025. 

.2 -.002.                     .0001-200.  .0004-250000. 

.2 -.2.                         10 -.0002.  40-25000. 

.2  -  .200.                     .001  -  .00002.  4  -  .000025. 

20  +  2000.                    1000  -  .0002.  .00004  -  .000025. 


FRACTIONS  49 

22.  23.  24. 

33  +  11.  250-12500.  .08  +  16. 

.0033  +  1100.  2.5  •*•  .00125.  80  +  1600000. 

33000  -#•  .0011.  2500  +  .0000125.  8000  -*-  .000016. 

3300  +  110000.  .00025  +  125000.  .0008  +  .00016. 

.33  +  .000011.  2.5  +  125.  .00008  •*•  16000. 

.00033  +  110000.  .025  +  .000125.  8  +  1600. 

.00033  +  .011.  .0025  + 1250000.  80000  + 160. 

.0033  *  .000011.  25000  +  .0000125.  800  *  .000016. 

330  +  .00011.  .25  +  .000125.  .0008  *  160000. 

.000033  +  1100000.  250  +  12500000.  .000008  +  .0016. 

REDUCTION  OF  FRACTIONS 

77.  Fractions  may  be  written  as  decimals  or  as  common 
fractions. 

Principles. — 1.  A  fraction  is  an  indicated  division. 

2.  The  denominator  of  a  decimal  when  expressed  is  1  with 
as  many  ciphers  annexed  as  there  are  orders  of  units  at  the 
right  of  the  decimal  point. 

PROBLEMS 

1.  Write  .64  as  a  common  fraction. 

2.  Write  TVo  as  a  decimal. 

3.  Write  .032  as  a  common  fraction. 

4.  Write  4  +  5   as   a  decimal.     Perform  the   operation  in 
dicated. 

5.  Write  £  as  a  decimal.     Perform  the  operation  indicated. 

6.  Write  J  as  a  decimal. 

Write  the  following  as  common  fractions : 

7.  .268,  10.   .0205.  18.   .0036. 

8.  .3758.  11.  .09.  14.  .25738. 

9.  .046.  ./#.   .049.  15.  .0013. 
Write  as  mixed  numbers : 

16.  2.65.  18.  10.15.  00.   101.101. 

,?7.   17.364.  19.  610.0018.  21.  13.085. 

Write  as  decimals : 

22.   f.  24.   |.  05.   f.  28.   |. 

05.    |.  05.  f.  07.   I.  00.  -|. 


50  MODERN   COMMERCIAL  ARITHMETIC 

NOTE.  —  When  the  division  is  not  exact,  the  remainder  may  be 
expressed  as  a  common  fraction,  or  the  sign  +  may  be  placed  after 
the  decimal  to  show  that  the  division  is  not  complete.  Thus,  J  =  .333J, 
or  .3333-f. 

Common  fractions  in  their  lowest  terms  cannot  be  reduced  to  pure 
decimals  if  their  denominators  contain  any  prime  factors  other  than 
2  or  5. 

30.  I.  34.   A.  38.   ¥V  42.    I 

31.  f.  35.    ft.  39.   \%.  43.    5V 

^2.  f.  *0.  *V  40.  «.  44-  ih- 

S3.   f.  37.  «.  41.  A-  4S.  U. 

NOTE.—  .251  =  .25125.     .23?  =  .2375. 

46.  .17J.  48.   .27^.  50.   .24f.  52.   .96?. 

47.  .24f.  49.   .16f.  57. 

NOTE.  —  3  J  =  3.  3333  +.     4.  0|  =  4.  05. 


54.  7i  50.   14f.  5^.  25.0|  .  60. 

55.  17.0f.  57.  20.00f.  59.  9.0TV-  ^^. 

78.  Whole  numbers  may  be  written  as  fractions  thus: 

5x2  5x14  5x20 

5  =  --=  --  =  tt  --= 


Changing  a  whole  number  to  a  fraction  by  giving  a  denom- 
inator to  the  whole  number  is  simply  dividing  the  number  by 
that  denominator. 

If  a  number  is  changed  to  a  fraction  with  a  given  denom- 
inator, the  number  must  be  multiplied  by  that  denominator. 


PROBLEMS 

9 

V 

9 

1.     3=    '-. 

0 

*15=t. 

5.  11,-. 

V 

V 

V 

a.  12  =  -. 

4-    o  =  —  . 

6'"  18=2^ 

7.  Write  7  as  13ths.  10.  Write  5  as  36ths. 

8.  Write  16  as  30ths.  11.  Write  8  as  41sts. 

9.  Write  4  as  27ths.  12.  Write  12  as  120ths. 


FRACTIONS  51 

79.  Mixed  numbers  may  be  written  as  common  fractions 
thus: 

H-l  +  iorf.  7|-Y+|orY- 

NOTE.  —  Multiply  the  whole  number  by  the  denominator  of  the 
fraction,  add  the  numerator,  and  write  the  sum  over  the  denominator. 

PROBLEMS 

^ 

Write  as  common  fractions  : 

1.  7f  4-  15f  7.  120T6f.  10.  163¥V 

0.  12|.  5.  20|.  8.  25}f.  .n.  16ft. 

5.  6f.  6.  14ft.  &  62  TV  ^.  24r8T. 


80.  Common  fractions  may  be  written  as  whole  or  mixed 
numbers  thus  : 

1  =  64-3  =  2.         I  =  7  *  3  =  2f         *ft6  =  245  -*-  12  =  20ft. 
NOTE.—  Perform  the  operations  indicated. 

PROBLEMS 

Write  as  whole  or  mixed  numbers  : 
i.  i£.  4.  *i*.  7.  YJ.          ^ 


•  W-  - 


81.  Common  fractions  may  be  written  in  their  lowest  terms. 
12*6     2 

f  1  -  ^g  ^  g  -  ¥•  tf  **  Tl  *"  T¥- 

Principle.  —  Dividing  both  numerator  and  denominator  by 
the  same  number  does  not  change  the  value  of  the  fraction. 

NOTE.  —  If  both  terms  be  divided  by  their  greatest  common  divisor, 
or  by  as  many  successive  divisors  as  possible,  the  fraction  will  then  be 
expressed  in  its  lowest  terms 

PROBLEMS 
Write  the  lowest  terms  of  the  following: 

*•  H-        4.  if         r.  m-        10.  m 

2.  H.  5.   rfft.  8.  TY*V  11.   H*. 

3.  iVV  6.   jffr.  9.  |41|.  12. 


52  MODERN    COMMERCIAL   ARITHMETIC 

82.  Common  fractions  may  be  written  in  higher  terms, 


3x3  5  x  6        ' 

Principle.  —  Multiplying  both  terms  of   a  fraction   by  the 
same  number  does  not  change  the  value  of  the  fraction. 
Thus,  change  $  to  27ths. 


27  9  x  3  "  *T* 

NOTE.  —  Multiply  both  terms  of  the  fraction  by  a  number  that  will 
change  the  given  denominator  to  the  required  denominator.  To  find 
such  a  number,  divide  the  required  denominator  by  the  given  denom- 
inator. 

PROBLEMS 

Change  : 

1.  TV  to    48ths.  5.     f  to  147ths.  9.  ||  to      72ds. 

2.  T5T  to    SOths.  6.  TV  to  225ths.  10.  f  f  to    319ths. 
8.  T9T  to    55ths.  7.  T<V  to  182ds.  11.  \\  to  3104ths. 
4.  if  to  105ths.  8.  ft  to  475ths.  12.  -fa  to    196ths. 

83.  Fractions  that  have  similar  denominators  are  similar 
fractions. 

84.  The  denominator  of  similar  fractions  is  a  common 
denominator. 

85.  The  leaet  or  lowest  denominator  that  similar  fractions 
can  have  is  their  least  common  denominator. 

86.  A  common  denominator  contains  each  of   the  given 
denominators. 

87.  The  least  common  denominator  that  two  or  more  frac- 
tions can  have  is  the  least  number  that  will  exactly  contain  the 
denominators  of  the  given  fractions. 

88.  Fractions   may  be    reduced  to   their   least    common 
denominator. 


FRACTIONS  53 

EXAMPLE. — Find  the  least  common  denominator  of  -J,  T^, 
TV,  andTV 

NOTE. — The  least  common  denominator  is  the  least  number  that 
will  exactly  contain  6,  12,  16,  and  18,  and  may  be  found  as  follows: 

OPERATION  EXPLANATION.— Write  the  num- 

bers as  here  shown.     Divide  suc- 

2  I  6,  12,  16,  18  cessively  by  any  prime  factor  that 

3~|~3 (3      3      9  will  be  contained  in  at  least  two 

of  the  numbers  to  be  divided.  The 

'     *       '       *  product  of  the  successive  divisors 

1  •     4,     3  and  the  remaining  numbers  that 

have  no  common  divisors  is  the 
2x3x2x4x3  =  144,  L.  C.  D.      L.C.D. 

PROBLEMS 
Find  the  L.C.D.  of  these  fractions: 

i-  f>  t,  I,  A-  ^  A,  A,  *38,  A- 

^-  i>  I  >  T\>  A'  ^-  i»  A»  A*  A- 

5-  A,  A,  A>  H-  6-  A,  T6*,  A,  A- 

89.  To  change  fractions  to  fractions  having  their  L.C.D. 
/.  Find  the  L.C.D. 

77.  Change  each  fraction  to  a  fraction  having  the  L.C.D.  as 
its  denominator. 

PROBLEMS 
Change  to  fractions  having  their  L.C.D. 

i-  H,  A,  A,  4-  7.  T'8,  &,  A,  ii,  W- 

«•  4,  A,  A,  li-  5-  A.  A,  A,  A- 

*•  A,  A.  ii  If-  9-  H»  if'  H»  «• 

^.  A,  A,  *l,  H-  ^.  H,  |f,  if,  if,  if. 

5.  A,  it,  A,  A  ^-  +,  U,  A,  !*»• 

e.  A,  H,  A,  *+•  ^-  H,  If,  Ai  A- 

MENTAL  PROBLEMS 
Reduce  to  their  simplest  forms: 

J.  H-         -4-  i"A.          7.  Ty8-          10.  T»A.          15.  |f 
*.  AV        5.  if-  5-  ti  11 


54 


MODERX    COMMERCIAL    ARITHMETIC 


Reduce  : 

M.  4  to  9ths. 
17.  J  to  18ths. 

£0.  J  to  72ds. 
27.  I  to  64ths. 

«*- 

05. 

|  to  120ths. 
/T  to  126ths 

18.  |  to  40ths. 
19.  ft  to  96ths. 

00.  4  to  49ths. 
05.  TV  to  55ths. 

.  07. 

}  to  70ths. 
A-  to  200ths. 

Reduce  to  integers 

or  mixed  numbers: 

28.  -H°.          31.   y. 
29.  i|A.          50.  ff 

Q  /        160                     QV 
3  Jf..      32  •                «»«• 

¥. 

#>•  W- 

^.  w- 

42.  *•%&. 

Reduce  to  the  fractional  form  : 

44-  n  •            -47-  2i- 

50.   12f           55. 

124. 

55.   15J. 
56.   10|. 
57.   144. 

58. 
5P. 
60. 


Find  the  L.  C.  D.  of: 
i  and  TV-  ^.  i 

J  and  ft-  63-  t  and  "A- 

ft  and  ^V  04-  A  and  ^. 

ft  and  A-  05.  TV  and  ft. 


69.   |, 


i,  and 
i,  and  T 
^,  and 


ADDITION   OF   FEACTIONS 

9O.  Principles.  —  1.  Only  similar  fractions  can  be  added. 
2.  Dissimilar  fractions  must  be  reduced  to  similar  fractions 
before  they  can  be  added. 

PROBLEMS 
EXAMPLE  1.  —  Find  the  sum  of  |,  |  and  ft. 


-  TV  A,*,  H- 

ti  4,  A,  A- 

*,  i»  A,  A- 
VS  V,  H,  U- 
fi>  H,  W>  H- 


Find  the  sum  of  : 
1.  i,  M,  TV 

^.  t,  I,  i,  H- 

^.  i  A,  A,  H- 

4-  I,  *,  T6.,  A- 

5-  ft,  A,  ^  A- 


FRACTIONS  55 

EXAMPLE  2.  —  Find  the  sum  of  3£,  7|,  6|,  and  5f  . 


=  21.     21  +  Iff  =  224f  . 
NOTE.  —  Add  fractions  and  integers  separately,  then  add  the  results. 

11.  124,  6if,  15H-  #•   82^,  1*A,  13H- 

12.  123f,  168&,  64^,  65TV         16.   3^T,  9H,  4&,  ^. 
IS.  27M,  19H,  45*V,  90/r-  ^   6A>  H»  28A,  63H, 


SUBTRACTION  OF  FRACTIONS 

91.  Principles.  —  1.  Only  similar  fractions  can.  be  sub- 
tracted. 

2.  Dissimilar  fractions  must  be  reduced  to  similar  fractions 
before  they  can  be  subtracted, 

PROBLEMS 
EXAMPLE  1.  —  Find  the  value  of  f  -TV 

|-iV  =  M-H=*V 

Find  the  value  of: 

i-  I-T'T-  •*.  A  -A. 

*.  !-T\.  5.  t-H. 

5.  n-M-  <?•  A-H. 

Mixed  numbers  may  be  reduced  to  improper  fractions. 
7.  3J-J.  W.   5| 


Fractions  and  integers  may  be  subtracted  separately. 

EXAMPLE  2.  —  Find  the  value  of  14|  -  11TV 

OPERATION  EXPLANATION.  —  Reduce  the  frac- 

\  —  A  =  If  ~~  f  f  tions  to  similar  fractions,     f  g  cannot 

143     =  1434  be   subtracted    from    fg,    therefore 

ji  9    =  11  JU  take  1,  or  fg,  from  14  and  unite  it 

with  f  g,  making  }g.    Then  subtract. 
n-H  =  «-     13  (14-1)-  11  =  2. 

^-   68/T-19H. 

^. 
15.  231|-193.  18. 


56  MODERN    COMMERCIAL    ARITHMETIC 

MENTAL  REVIEW  OF  ADDITION  AND   SUBTRACTION 
93.  To  add  two  fractions  whose  numerators  are  each  1,  take 
the  sum  of  the  denominators  for  the  numerator,  and  the  prod- 
uct of  the  denominators   for  the   denominator  of   the  •  sum. 
Thus,  }  +  i  =  A. 

Find  the  value  of  : 

1.   1+f  6.  i+f  11.   i  +  f 

*•   *  +  *•  ?•  ^  +  4.  12. 

IS. 


5.   i+TV.  10.   i  +  f,  15.   i  +  f 

93.  To  subtract   fractions  whose  numerators  are  each  1, 
take  the  difference  of  the  denominators  for  the  numerator  and 
the  product  of  the  denominators  for  the  denominator  of  the 
remainder.     Thus,  £  —  -J-  =  ?V 

Find  the  value  of: 

1.   i-f  5.  i-f  9.  t-i. 

2-    J-i-  <*•  i~J.  *>•   i-i- 

5.    l-f  7.  i-A-  ^   »-«• 

^.   i-f.  <?.  ^-1.  ^.   t-J. 

94.  To  add  two  fractions  whose  numerators  are  greater  than 
1,  take  the  sum  of  the  products  of  the  numerators  of  each  by 
the  denominator  of  the  other  for  the  numerator,  and  the  prod- 
uct  of   the   denominators   for   the   denominator  of  the   sum. 
Thus,  f  +  i  =  «. 

2  x  4  +  3  x  3  =  17  and  3  x  4  =  12. 
Find  the  value  of: 

1-  f  +  t-  S.  |  +  f.  9.   i  +  f. 

*.  f  +  f.  6.  f  +  j.  10.   f+I. 

^.   f+I-  7.  f  +*.  H.  I  +  A. 

4.  f+f  *.  |  +  |.  i*.  4+i 

95.  To  subtract  two  fractions  whose  numerators  are  greater 
than  1,  take  the  difference  of  the  products  of  the  numerator  of 
each  by  the  denominator  of  the  other  for  the  numerator,  and 
the  product  of  the  denominators  for  the  denominator  of  the 
remainder.    Thus,  f  -  f  =  TV-    (3x3-2x4=1,  and  3x4=  12.) 


FRACTIONS  57 


Find  the  value  of : 

i*  i-i 

2.  f-T3T. 


'         7            3 
I         _L  3 

9.  1  -3- 

;-   l-t- 

*>•  A-f 

'•  i-i 

^.  4  -!• 

'•   f-f 

i*.  I  -f 

MULTIPLICATION  OF  FRACTIONS 

96.  Principles.  —  1.  Multiplying  the  numerator  multiplies 
the  fraction. 

2.  Dividing  the  denominator  multiplies  the  fraction. 

PROBLEMS 

Find  the  product  of: 

1.  \  x  2,  or  2  x  f  . 

f  x  2  =  ^y?  =  f     (Principle  1.  ) 

2.  f  x  4,  or  4  x  f.  5.  T9^  x  7,  or  7  x  -fy. 

3.  T\  x  6,  or  6  x  TV  6.  T8T  x  4,  or  4  x  ^T. 

4.  T\  x  8,  or  8  x  T\.  7.  |f  x  6,  or  6  x  f  |. 


x  3,  or  3  x 


x  3  =  =  *'     (PrinciPle  2-  ) 


9. 

Jf  x  9,  or  9  x  fj. 
ff  x  12,  or  12  x  ff. 

if  x  17,  or  17  x  if. 

^.  i 
^  i 

5?T  x  3,  or  3  x  ^T. 
j  x  21,  or  21  x  Jf 
VfXll,  or  11  x^ 

75. 

fxf 

• 

AX 


58 


MODERN    COMMERCIAL   ARITHMETIC 


Mixed  numbers  may  be  reduced  to  improper  fractions. 
M.  If  x  2|  x  3f  24.  &  x  2ft  x  3ft. 


23. 


25. 


EXAMPLE  1.— Find  the  product  of  12f  x  14  or  14  x  12f . 

OPERATION 


14 
168 

Bf 
176| 


EXPLANATION. — Multiply  the  integral  and  the 
fractional  parts  of  the  mixed  number  separately 
by  the  whole  number,  and  add  the  products. 
12  X  14  =  168.  f  X  14  =  8§.  168+  8|  =  176§. 


26.  14fxl8. 

27.  13T6Txl4. 

28.  15xl2f. 

29.  42x7T\. 
SO.  62T6Tx21. 

31.  135ft  x  48. 

32.  206ft  x  56. 


33.  89x17^- 

34.  156x4  ft. 

35.  73x62|. 
86.  28T6Tx45. 

37.  35T%x39. 

38.  64y\x75. 

39.  56fxl4. 


40.  48fx25. 

41.  31xl4|. 

42.  44xl6T\. 

43.  39xl2TV 
44-  17x23if. 
45.  SlxlSff- 


EXAMPLE  2. — Find  the  product  of  12£  x  15J. 
OPERATION 

2t 

H  NOTE.— The  connecting  lines  in  the  diagram 


180    =12x15          show  the  steps  in  the  operation. 
7i=   |x!5  P\/h 

\llll  UX^ 


191f  =  12i  x 


46.  16TVxl4|. 

47.  128T3T  x  42|. 

48.  169ft  x  28ft. 

49.  54|x72|. 


50.  24|x36|. 

51.  180|^xl4f. 

52.  1684|  x  132| . 

53.  426ft  x  96 1 . 


54.  28ftx26-|. 

55.  33/TxllJ. 

56.  7fxl46|. 

57.  18|xl20J. 


FRACTIONS  59 

MENTAL  PROBLEMS 
Find  the  product  of : 

1.   fx7.  U.  45  x$.  27.  ix-ft-  39.  &  x  •&• 

&   |  x  18.          15.  T<V  x  84.  28.    1/  x  y.  40.  -ft  x  T\. 

5.  |x27.          ./6'.   fx!5.  £0.'fxV-  4-?-  fxfxf 

4-  fx35.          77.   1x17.  30.   AxH*-  4&  i  x  |  x  TV 

5.  |  x  12,          #.   |  x  16.  31.   I  x  f .  ^.  4  x  A  x  f . 

0.  T4T  x  44.        m   49  x  f .  30.  T\  x  ff.  44-  |  x  *  x  if 

7"        5     sx  ft£  ®f}      1  flQ  \x  8  QQ      3   v  2  8  LZ      Ss/lvS 

/ .    Y%  X  00.  /v(/.     lUo  X  ^.  Ot>.     ^-  X  y-g .  ^tt>.     §  X  ^  X  ^. 

5.  |x64,  21.   fxf.  54.   AX  A-  -*«.  ixfxf. 

9.  SSx^j.  ^.    |x|.  35.  A* A-  ^7-  T3irx|xf 

10.  56  x|.  .  «».  fxff  56.  Ax|f.  4*.  *xfxf. 

11.  32  x  A-  ^-  *xA-  57-  4XV-  ^-  |x>xf 
^.  20x4.  25.   Ixi.  55.   T\  x  1.  50.  JLxA-xj. 

O  o»  lies  l«SJlo 

^.  30x3.          ^0.  AX  A. 

o  1  A  o  0 

DIVISION  OF  FEACTIONS 

97.  Principles. — 1.    Dividing   the   numerator  divides  the 
fraction. 

2.  Multiplying  the  denominator  divides  the  fraction. 
EXAMPLE  1. — Find  the  quotient  of  Tf  -f- 6. 

OPERATION 

12 -j- 6  EXPLANATION. — To   divide   }J    by  6 
If  •*•  6  =     17     =  TST-    Or,      is  to  take  i  of  j j     t|  x  J  =  ft.    But  ^ 
12                              is  f  inverted,  and  f  is  the  divisor  writ- 
is.  _._  g  _ .  _  ^2^  =  ^.       ten  as  a  fraction.     Hence  if  we  write 

1 '  x  6  the  (jivisor    as   a  fraction,   invert  the 

divisor,  and  multiply  the  dividend  by  the  inverted  divisor,  we  divide 
by  the  divisor.  Then,  to  divide  by  a  fraction,  invert  the  divisor  and 
multiply. 

NOTE. — Divide  when  you  can,  multiply  when  you  must. 

PROBLEMS 
Find  the  quotient  of : 

1.  ||-5.                     6.  ff-6.  11.  Jf*18- 

2.  §3-9.                     7.  ff  -4-4.  12.   ^yt  +  26. 

3.  if -16.                   8.  T\-4.  13.  -fi-27. 

4.  tt  +  8.                     9.  |f +  9.  •                  1£.   H  +  8. 

5.  ^-6.                    /#.  T^-3.  75.   H-3. 


60  MODERN    COMMERCIAL    ARITHMETIC 

Mixed  numbers  may  be  changed  to  improper  fractions. 

16.  l£f-f-3.  18.   2f-3.  20.   4f-f-5. 

17.  3H  +  15.  19.  5TV  +  17.  21.   If +  6. 

EXAMPLE  2.— Find  the  quotient  of  19J  -*-  6. 

OPERATION          EXPLANATION. —6  is  contained  in  19  three  times,  with 
a  remainder  of  1.      Change   1   to   \   and   add   it   to   |, 

3^\         making  \.     \  divided  by  6  is  /?. 

NOTE. — Instead  of  reducing  the  mixed   number  to  an  improper 
fraction,  it  is  sometimes  more  convenient  to  divide  as  above. 

22.  129|  +  8.  26.  17|  +  7.  30.  57-ft  +  S. 

23.  1384^-5  27.  31T6F  +  5.  31.  268TV  +  H 

24.  21f  +  6.  28.  43T4T.  32.   78561  +  7. 

25.  3804  +  10.  29.   15f  +  9.  33.   12032/T-15. 
NOTE. — Invert  the  divisor  and  multiply. 

S5.  4  +  14-  39.   lA-f.  43.   123T8T-65J. 

0/y       164  7/2.4  /  ^T       Q  4    •    2 

O  i  .     ir¥    -f-  Tf.  JfJ..     -y -I    —  VV .  JfU .      O-g-  ~^~   3^  • 

Divide: 

^.    fV  of  T8T  by  |  of  44.  50.  f  of  |  by  f  of  f  of  if. 

47.  A  of  if  by  ||  of  rV8.  51.  if  of  if  by  \\  of  if. 

4^.   3|  of  2TV  by  |f  of  if  50.  4|  of  6T8T  by  4|  of  5|. 

40.  11-fr  of  14T3T  by  2J  of  f  |.  55.  ||  of  H  ty  4t  of  H- 

MENTAL  PROBLEMS 
Find  the  quotient  of : 

1.  _?T^3.  ^.  8  +  4.  ^.  J  +  f  ^.  12  +  f. 

^.  ^f-4-6.  ^.  9  +  -^.          ^.  f +  f.  50.  7  +  |. 

3.  fi+7.  ^.   12  + A-        ^-  *  +  A-          ^-  *•*•»• 

4.  -^  +  5.        14.  15  +  f        04.  i  +  f.          54.  |  +  Tv 

5.  6^.6>  75.  25  +  2f  ^5.  f+|.  55.  f+f|. 

^.  T6T-15.  ^.  18 +  |.  0<5.  16  +  |.  ^-  4-i 

7.  T\-14.  17.   J+15.  07.  |  +  9.  57.  T\-i- 

^.  Y^4.  -/5.  24  +  |.  28.  ^ +  3.  &?.  4  +  9. 

9.  if-lO.  70.   30  +  f.  ^-  t  +  f  ^-  15  +  4. 

70.  6  +  f  00.  f  +  8.  '  50.  f  +  f .  40.  24  +  f . 


OF  THE 

UNIVERSITY 

OF 

FRACTIONS  61 

THE  THREE  PROBLEMS  OF  FRACTIONS 
98.  1.  To  find  a  part  of  a  number:    What  is  £-  of  48? 

2.  To  find  what  part  one  number  is  of  another:   6  is  what 
part  of  15? 

3.  To  find  a  number  when  a  part  of  it  is  given :  f  of  a  num- 
ber is  12;  what  is  the  number?  12  is  f  of  what  number? 

Solution  by  the  Equation 

Each  of  the  above  problems  may  be  stated  as  an  equation. 
Is  means  =,  of  means  x.     Representing  the  number  to  be 
found  by  ?,  the  above  problems  may  be  stated  thus : 

I.  ?  =  £x48.          2.  6  =  ?xl5.          3.  f  x?  =  12;  12  =  |  x  ?. 

In  equations  2  and  3,  the  product  of  two  numbers  and  one 
of  the  numbers  is  given  to  find  the  other  number. 

PROBLEMS 

Write  each  of  the  following  problems  as  an  equation  and 
then  solve  the  equation : 

1.  Findf  of  270.     (?  =  fx270.) 

2.  21  is  what  part  of  36?    (21  =  ?x36.) 
8.  Of  48,  27  is  what  part?    (27  =  ?  x  48.) 

4.  25  is  f  of  what  number? 

5.  f  of  a  number  is  35 ;  what  is  the  number? 

6.  What  is  T\  of  128? 

7.  342  is  |  of  what  number? 

8.  T65-  is  f  of  what  number? 

9.  Of  T4s,  -fa  is  what  part? 
10.  What  is  |f  of  180? 

II.  What  part  of  86  is  14? 
12.  What  part  of  32f  is  12£? 
18.  Of  64£  days,  f  is  what  part? 

14.  18|  is  •£$  of  what  number? 

15.  24£  pounds  is  what  part  of  65£  pounds? 

16.  A  cow  cost  27f  dollars,  and  a  horse  78^-  dollars.      The 
cost  of  the  cow  was  what  part  of  the  cost  of  the  horse? 


62  MODERN    COMMERCIAL    ARITHMETIC 

17.  A  desk  cost  18f  dollars,  which  was  T9i  of  the  cost  of  a 
table.     What  was  the  cost  of  the  table? 

18.  The  value  of  26  cords  of  wood  at  3f  dollars  per  cord  is 
what  part  of  the  value  of  35  tons  of  coal  at  4|  dollars  per  ton? 

19.  A  gain  of  /r  of  a  stock  of  goods  is  a  gain  of  what  part  of 
£  of  the  goods? 

20.  Different    kinds  of    coffee  are  mixed  in  the   following 
parts:    14y5F  pounds,  18T\  pounds,  21T4F  pounds.    Each  part  is 
what  part  of  the  whole  mixture? 

21.  If  31£  gallons  of  cider  make  of  gallons  of  jelly,  the 
number  of  gallons  of  jelly  is  what  part  of  the  number  of  gallons 
of  cider? 

MENTAL  REVIEW 

99.  Solve  mentally : 

1.  Add  \  and  ^ . 

2.  From  ±  take  f 

8.  Add  J,  i,  t  and  f 

4.  Find  the  product  of  £,  -^,  •£,  |  and  |. 

5.  Change  T\  to  84ths. 

#.  Reduce  \$%  to  lowest  terms. 

7.  What  will  12  pounds  of  tea  cost  at  f  dollars  per  pound? 

8.  What  will  -&  of  a  ton  of  hay  cost  at  $18  per  ton? 

9.  Find  the  cost  of  9  ounces  of  butter  at  $.20  per  pound. 

10.  Find  the  cost  of  15  eggs  at  $.14  per  dozen. 

11.  If  1  pound  14  ounces   of  cheese  cost  $.23,  what  is  the 
price  per  pound? 

12.  If  a  horse  eats  f  bushel  of  oats  in  a  day,  how  long  will  30 
bushels  last  him? 

IS.  Divide  14  by  4? 

14.  A  crock  of   butter  weighs  8£  pounds,  and  the  crock 
alone  weighs  1^  pounds.     What  is  the  value  of  the  butter  at 

cents  per  pound? 

15.  What  will  9|  cords  of  wood  cost  at  4|  dollars  per  cord? 

16.  At  36  bushels  to  the  acre,  what  is  the  yield  of  1$  acres? 

17.  |  is  what  part  of  f  ? 


FRACTIONS  63 

18.  What  is  T\  of  32? 

19.  18  is  what  part  of  40? 

20.  From  |  take  -J. 

^^.  Find  the  cost  of  f  of  a  piece  of  cloth  of  36  yards  at  1^ 
dollars  per  yard. 

22.  At  If  dollars  per  day  of  10  hours,  what  will  a  man  earn 
in  7£  hours? 

23.  If  10  bushels  of  apples  will  make  32  gallons  of  cider, 
how  much  cider  will  7  bushels  make? 

24.  Find  the  cost  of  750  feet  of  lumber  at  9J-  dollars  per 
thousand. 

25.  |  is  what  part  of  -y~? 

26.  A  lady  bought  5f  yards  of  silk  for  8|  dollars,  what  was 
the  price  per  yard? 

27.  At  If  dollars  per  yard,  how  much  cloth  can  be  purchased 
for  $14? 

28.  32  is  £  of  what  number? 

29.  What  part  of  64  is  42? 
80.  |  is  what  part  of  f  ? 

31.  A  grocer  mixed  7  ounces  of  coffee  at  $.  30  per  pound 
with  9  ounces  at  $.40  per  pound.  What  is  the  pound  of  mixed 
coffee  worth? 

82.  Divide  T\  by  8. 

88.  Add  f  and  f . 

34.  A  couch  is  worth  $9.    For  how  much  must  it  be  sold 
to  gain  Ty 

35.  At  $4.50  per  week,  what  will  five  days'  board  cost? 

86.  Sold  a  book  for  $2.25  and  gained  f .  What  did  the  book 
cost  me? 

37.  Find  the  cost  of  f  of  a  yard  of  silk  at  $.60  per  yard. 

88.  14  is  what  part  of  7? 

89.  Multiply  f  by  6. 

40.  15  is  .75  of  what  number? 

41.  Find  the  cost  of  .8  pounds  of  tea  at  $.45  per  pound. 
J$.  Find  the  cost  of  f  of  a  ton  of  coal  at  $6.50  per  ton 
43.  Change  f  to  a  decimal. 

44-  Change  .  625  to  a  common  fraction. 


64  MODERN    COMMERCIAL   ARITHMETIC 

45.  Bought  a  wagon  for  $40  and  sold  it  at  a  gain  of  .20  of 
the  cost.     Find  the  selling  price. 

46.  If  I  wish  to  gain  $.25  on  a  dollar,  how  must  I  mark  an 
article  that  cost  me  $4.80? 

47.  Sold  a  table  for  $6  and  made  a  gain  of  .25  of  the  pur- 
chase price.     Find  the  purchase  price. 

48.  Find  the  cost  of  425  pickles  at  $.30  per  hundred. 

49.  Change  -fc  to  a  decimal. 

50.  |  is  what  part  of  .40? 

51.  Change  .2£  to  a  common  fraction. 

52.  A  man  borrows  $350,  and  agrees  to  pay  .06  of  the  sum 
for  its  use.     How  much  should  he  pay  the  lender? 

53.  .08  is  what  part  of  .16? 

54.  At  $.  12£  apiece,  how  many  brushes  can  be  bought  for 
4f  dollars? 

55.  In  selling  combs  at  $.20,  I  lost  .20  of  the  cost.    What 
did  they  cost  me? 

56.  What  is  .04  of  f  ? 

57.  |  is  what  part  of  .80? 

58.  Find  the  cost  of  10  ounces  of  meat  at  $.12£  per  pound? 

59.  A  rod  10  feet  long  is  lengthened  by  .03  of  itself.    What 
is  its  length  then? 

WEITTEN   REVIEW 

1OO.  Solve  the  following: 

1.  If  a  furnace  consumes  a  ton  of  coal  in  9  days,  in  how 
many  weeks  will  it  consume  9  tons? 

2.  If  I  pay  $36.40  with  wheat  worth  $f  per  bushel,  how 
many  bushels  must  I  give? 

3.  If  a  train  goes  146.54  miles  in  3  hours,  what  is  the  rate 
of  speed  per  minute? 

4-  A  contributed  $5800  to  the  capital  of  a  company;  B, 
$7800;  C,  $9600;  and  D,  $5500.  What  part  of  the  whole  did 
each  put  in? 

5.  From  a  tract  of  49-f-  acres  of  land,  how  many  lots  of  f  of 
an  acre  each  can  be  laid  out? 


FRACTIONS  65 

6.  A  agreed  to  keep  B's  horse  14  weeks  for  $18.    If  A  keeps 
the  horse  11  days,  how  much  ought  B  to  pay? 

7.  A  field  of  29£  acres  produced  3450  bushels  of  potatoes. 
What  was  the  average  yield  per  acre? 

8.  At  $.87£  per  bushel  of  60  pounds,  what  will  4780  pounds 
of  wheat  cost? 

9.  If  apples  lose  .70  of  their  weight  in  drying,  how  many 
pounds  of  apples  must  be  used  to  make  300  pounds  of  dried 
apples? 

10.  If  a  bushel  of  wheat  of  60  pounds  will  make  44  pounds 
of  flour,  and  16  pounds  of  feed,  and  the  miller  takes  .10  of  the 
grist  for  grinding,  how  many  bushels   of  wheat  must  a  cus- 
tomer take  to  the  mill  to  get  10  barrels  of  flour  of  195  pounds 
each?     How  much  feed  will  he  get? 

UNITED  STATES  MONEY 

101.  Money    is    a  measure  of    value   and    a  medium  of 
exchange. 

A  watch  is  worth  10  dollars.  The  dollar  is  the  unit  of 
measure. 

A  piece  of  cloth  is  10  yards  long.  The  yard  is  the  unit  of 
measure. 

A  butcher  wants  a  hat  worth  3  dollars,  a  ring  worth  5  dol- 
lars, and  a  book  worth  3  dollars.  Can  he  take  3  dollars'  worth 
of  meat  to  the  hatter,  5  dollars'  worth  to  the  jeweler,  and  3 
dollars'  worth  to  the  bookseller  and  exchange  for  the  things  he 
wants?  Why?  What  can  he  do  that  he  may  practically  ex- 
change his  meat  for  these  things?  Why  does  the  butcher 
exchange  his  meat  for  money  if  they  both  have  the  same  value? 
Money  is  the  medium  by  which  the  butcher  makes  the  exchange. 

102.  The  unit  of  United  States  money  is  the  dollar. 

The  first  Congress  of  the  United  States  made  the  dollar  the 
unit  of  value.  It  determined  the  value  of  the  dollar  by  pro- 
viding for  the  coinage  of  silver  dollars  to  contain  371.25  grains 
of  pure  silver  (with  certain  alloy)  and  of  gold  pieces  to  contain 
24.75  grains  of  pure  gold  (with  certain  alloy)  to  the  dollar. 


66  MODERN    COMMERCIAL    ARITHMETIC 

The  value  of  the  coins  was  determined  by  the  amount  of  metal 
they  contained,  and  by  the  value  trade  and  custom  gave  them. 
The  coin  determined  the  value  of  the  dollar,  the  dollar  did 
not  determine  the  value  of  the  coin. 

103.  Ratio. — By  the  first  coinage  law  the  weight  of  a  silver 
dollar  was  15  times  the  weight  of  a  gold  dollar.     The  ratio  of 
weight  then  was  15  to  1.     In  1836,  Congress  passed  a  bill  mak- 
ing the  coinage  ratio  16  to  1,  so  that  since  then  a  silver  dollar 
weighs  16  times  as  much  as  a  gold  dollar. 

104.  The  denominations  and  scale  of  United  States  money 
are  shown  by  the  following 

TABLE 

10  mills     =  1  cent  (0,  c.,  or  ct.). 
10  cents     =  1  dime. 
10  dimes   =  1  dollar  ($). 
10  dollars  =  1  eagle. 

United  States  money  is  based  on  the  decimal  scale.  It  is 
expressed  as  dollars,  cents,  and  mills.  The  terms  dime  and 
eagle  are  not  commonly  used.  Dollars  are  written  as  integers, 
cents  as  hundredths,  and  mills  as  thousandths. 

The  sign  ($)  is  prefixed  to  expressions  of  United  States 
money;  as,  $7,  $.07,  $.007. 

Cents  and  mills  are  sometimes  written  as  common  fractions ; 
as,  $12.25,  $12rV<r,  16^,  $12£,  or  $.165. 

If  the  final  result  of  a  computation  contains  five  or  more 
mills,  they  are  counted  as  one  cent;  if  less  than  five,  they  are 
rejected;  as,  $3.166,  $3.17;  $4.714,  $4.71. 

United  States  Coins 

105.  Gold:    The  double-eagle,  eagle,  half -eagle,  and  one- 
dollar  piece. 

Silver:  The  dollar,  half-dollar,  quarter-dollar,  and  the  ten- 
cent  piece. 

Nickel:  The  five-cent  piece. 
Bronze:  the  one-cent  piece. 


UNITED    STATES   MONEY  67 

At  various  times  other  pieces  have  been  coined;  as,  the 
half -cent  and  the  two-cent  piece  in  bronze,  the  nickel  three- 
cent  piece,  the  silver  half-dime,  silver  twenty-cent  piece,  silver 
trade -dollar,  three-dollar  gold  piece. 

106.  Alloy. — All  coins  contain  an  alloy  to  toughen  them 
and  reduce  the  loss  from  abrasion.     Gold  coins  are  made  of  ^ 
pure  gold  and  TV  silver  and  copper.     Silver  coins  are  made  of 
T\  pure  silver  and  TV  copper.     Nickel  coins  are  made  of  f  cop- 
per and  \  nickel.     The  bronze  coins  are  made  of  TW  copper 
and  Tf  ^  tin  and  zinc. 

107.  Legal  Tender. — Money  that  when  offered,  or  tendered, 
in  payment  of  a  debt  must  be  accepted  or  lose  further  interest  is 
called  a  Legal  Tender.     Gold  coins  and  silver  dollars  are  legal 
tender  for  all  debts ;  the  other  silver  coins,  for  debts  not  exceed- 
ing $10;  the  other  coins,  for  debts  not  exceeding  25$. 

United  States  Paper  Money 

108.  United  States  paper  money  consists  of  notes,  gold  and 
silver  certificates.     A  note  is  a  promise  to  pay.     Its  value  con- 
sists in  the  promise  to  pay.     Notes  given  by  some  men  are  good, 
notes  given  by  some  men  are  worthless.     In  what  is  the  differ- 
ence?    The  notes  of  the  United  States  government  are  good. 
Why? 

United  States  notes  are  called  Greenbacks  and  Treasury 
Notes.  Examine  one  or  more  of  each.  Eead  what  is  printed 
on  them.  Why  are  they  as  good  as  gold? 

National  Bank  Notes,  or  Bank  Bills,  are  issued  by  national 
banks  under  the  supervision  of  the  United  States  government. 
These  bills  are  not  legal  tender,  but  they  are  redeemable  in 
lawful  money.  Examine  a  bank  bill.  Why  are  they  received 
for  debts? 

Certificates  of  Deposit  are  called  Gold  Certificates  and  Silver 
Certificates.  Examine  one  of  each.  Are  they  legal  tender? 
Why  are  they  received  for  debts? 

109.  Coin  is  metallic  money.      Currency  is  any  kind  of 
paper  money. 


68  MODERN    COMMERCIAL   ARITHMETIC 

OPERATIONS  WITH  ALIQUOT  PARTS 

Aliquot  Parts 

110.  The  Aliquot  Parts  of  a  number  are  the  parts  that 
will  exactly  divide  the  number.     Thus,  2,  2£,  3*,  are  aliquot 
parts  of  10. 

Aliquot  parts  of  10,  100,  1000,  respectively: 

(5  C      3*  (      3*  (If 

Halves-}    50       Thirds  J    33£       Fourths-]    25       Sixths  •!    16| 

(  500  (  333*  (  250  (  166* 

(      li  (  ( 

Eighths-^    12*        Twelfths  •{    8*         Sixteenths^    6£ 
(  125  (  83*  (  62i 

MULTIPLICATION  WITH  ALIQUOT  PARTS 

111.  EXAMPLE.—  Multiply  1836  by 


OPERATIONS  EXPLANATION.  -  33J  is 

1836x25  =1836  -4  x  100=  45900.  i  of  100.  Therefore,  the 
1836  x  *6t  -1836  +  6  x  100=  30600.  *  ired  duct  is  ^ 
1836  x  125  =  1836  -  8  x  1000  =  229500.  ,  Jny  hundreds  „  3  is 
contained  times  in  1836,  or  612  hundred,  or  61200. 

NOTE.  —  Take  such  a  part  of  the  multiplicand  as  the  multiplier  is 
of  1.0  and  annex  one  cipher,  as  the  multiplier  is  part  of  100  and  annex 
two  ciphers,  or  as  the  multiplier  is  of  1000  and  annex  three  ciphers. 


PROBLEMS 
Multiply: 

1.  1836  by  50,  25,  12|,  8J,  6£. 

2.  2448  by  50,  33£,  25,  16f  ,  12£,  8J,  6±. 

3.  368  by  50,  33£,  25,  16|,  12|,  8J,  6J. 

4.  42  by  3£,  33J,  33>3^,  2£,  25,  250. 
;>.  56  by  2^,  25,  250,  li,  m,  125. 
6\  486  by  If,  16*,  166*,  8*,  83*. 

7.  126  by  li,  12*,  125,  2*,  25,  250. 

8.  156  by  '-8*,  83*,  -2*,  25,  250,  33*. 

9.  256  by  6*,  62£,  8*,  83*,  25,  333*. 


ALIQUOT   PARTS  69 


10.  $26.40  by  50,  33£,  25,  16|, 

11.  $1.84  by  33£,  250,  16f,  125,  83£,  6£. 

72.  $3.36  by  5,  3£,  2£,  33J,  25,  If,  m,  !£,  16f,  125,  8J, 
62^,  83£,  6J,  50,  333£,  250,  166|. 

IS.  $7.68  by  If,  250,  16f,  25,  166f,  2|,  1^,  333£,  12|,  33$, 
125,  3i,  8i,  6f,  83^,  6£. 

74.  $10.56  by  62|,  6J,  83^,  125,  8J,  12|,  IGf  . 

15.  $50,  $.33^,  $.02^,  $.16f, 
$62.50,  $1.25  by  576. 

112.  Multiplication  Table 


2 

o 

6f 

101 

_L  /v"5" 

16f 

25 

33* 

3 

H 

10 

18f 

25 

37i 

50 

4 

10 

13* 

25 

33* 

50 

66f 

5 

12f 

16f 

31i 

41* 

/»<)  1 

U/v'2' 

saj 

6 

15 

20 

37| 

50 

75 

100 

7 

•17* 

423* 

43f 

58i 

87* 

116f 

8 

20 

2tff 

50 

66| 

100 

133* 

9  22|  30  ^56i  75   112^  150 
10  25   33^  62|  83i  125   166f 

NOTE  1.  —  This  table  can  bo  easily  learned  and  will  prove  conve- 
nient in  mental  operations. 

NOTE  2.  —  Black  figures  indicate  multipliers  and  multiplicands. 
Intersecting  points  of  horizontal  and  vertical  columns  give  the  prod- 
ucts. 


MENTAL  DRILL 

1.  Multiply  each  multiplicand  by  its  corresponding  multi- 
plier. 

2.  Multiply  each  multiplicand  by  each  of  all  the  multipliers. 

3.  Multiply  each  of  all  the  multiplicands  by  each  multiplier. 


70  MODERN    COMMERCIAL    ARITHMETIC 

MULTIPLICANDS         MULTIPLIERS          MULTIPLICANDS     MULTIPLIERS 

$  6.72  .05  $  .05  48 

7.20  .02|  .03J  96 

7.68  .03£  .33£  144 

8.16  .83J  .02|  192 

8.64  2.50  .25  240 

9.12  .16f  2.50  288 

9.60  .25  .16$  336 

10.08  .62£  1.66|  384 

10.56  1.25  .12£  432 

11.04  .33J  1.25  528 

12.96  1.66f  .83^  576 

13.44  .12^  .62|  524 

NOTE. — The  product  will  be  the  same  whichever  factor  is  used  as 
the  multiplier. 

DIVISION  WITH  ALiaUOT  PARTS 

113.  EXAMPLE.— Divide  245  by  3£,  33£,  and  333£  respect, 
ively. 

OPERATION  EXPLANATION.— 10  is  3  times  3J.     245  -*-  3 

245  -f-      3£  =  73. 5  equals  as  many  times  3  as  there  are  10's  in  245, 

245  -^    33£  =    7.35         or  24. 5.     24  5  X  3  ==  73. 5.     In  like  manner,  100 
245  -  333 £  =      .  735       is  3  times  33J,  and  1000  is  3  times  333^. 

NOTE. — To  divide  by  an  aliquot  part  of  10,  100,  or  1000,  multiply 
the  dividend  by  the  number  that  shows  what  aliquot  part  the  divisor 
is  of  10,  100,  or  1000,  and  point  off  1,  2,  or  3  places,  as  the  divisor  is 
part  of  10,  100,  or  1000. 

MENTAL  PROBLEMS 

1.  Divide  all  the  dividends  by  each  divisor. 

2.  Divide  each  dividend  by  all  the  divisors. 

DIVIDEND     DIVISOR      DIVIDEND       DIVISOR       DIVIDEND  DIVISOR 

.76  125 

1.82  8£ 

4.25  83J 

7.63  6i 
2.57 


7.82 

5 

87.64 

.83£ 

5.47 

50 

32.45 

1.25 

.82 

3* 

17.63 

.62-J- 

1.26 

33£ 

18.24 

1.66| 

3.14 

Q  1 

"2" 

5.67 

2.50 

ALIQUOT   PARTS  71 


DIVIDEND 

DIVISOR 

DIVIDEND 

DIVISOR 

DIVIDEND 

DIVISOR 

.91 

25 

4.39 

•i  Q  i 

•  -*-  &  2" 

14.75 

.33* 

.85 

250 

35.87 

.06^ 

7.53 

.50 

2.13 

16} 

42.64 

.25 

12.15 

.02* 

4.16 

166} 

3.65 

.08* 

8.24 

.03J 

.53 

1  O_L 

J./V* 

16.52 

.16| 

124.16 

.05 

PEJCE,  COST,  AND  QUANTITY 

114.  Business  computations  deal  with  price,  cost,  and 
quantity. 

Solution  by  the  equation:  Let  P  =  price,  C  =  cost,  Q  = 
quantity.  Then,  P  x  Q  =  C.  .Hence,  C  +  Q  =  P,  and  C  -*-  P  =  Q. 

MENTAL  PROBLEMS 

1.  If  the  price  is  8  cents,  and  the  quantity  12,  what  is  the 
cost? 

2.  If  16  articles  cost  48  cents,  what  is  the  price? 

3.  If  the  price  is  3  cents  and  the  cost  36  cents,  what  is 
the  quantity? 

Find  the  term  not  given: 

PRICE      QUANTITY      COST  PRICE    QUANTITY       COST 

4.  $.08  15  ?  10.  $.12*         16  ? 

5.  .11  ?          $1.32  11.       ?  21         $1.05 

6.  .12  10  ?  12.     .25  12  ? 

7.  .06  ?  2.40  IS.       ?  14  .98 

8.  ?  15  6.00  14.     .11  ?  1.65 

9.  ?  8  1.60  15.     .08  ?  4.00 

EXERCISES 
Tell  how  to  find  the  term  not  given . 

1.  P  (25#),  Q.  7.  C,  P. 

2.  P  (62*#),  C.  8.  C,  Q  (33*). 

3.  C,  Q  (12*).  9.  C,  P  (83*$. 

4.  C,  P  ($16}).  10.  Q,  P  ($2.25). 

5.  Q(112*),  P.  11.  P,  Q  (166}). 

6.  P  ($1.16}),  Q.  12.  C,  Q(62*). 


72  MODERN    COMMERCIAL    ARITHMETIC 

18.  P  (250),  C.  82.  Q,  P  (500). 

14.  C,  P  ($6.25).  83.  P  ($83 J),  0. 

15.  Q,  P  ($2.125).  &£.  Q  (6±),  C. 

16.  Q  (83*),  P.  85.  Q,  P  ($2.50). 

17.  Q  (25),  C.  86.  Q  (75),  P  ($2.33J). 

18.  C,  P  (66f0).  57.  Q,  P  (62i#). 
^.  Q  (33 *),  C.  £*.  Q  (83*),  C. 

20.  P  (750),  Q.  89.  C  ($1.66f),  P  (3£0). 

&/.  Q  (75),  P.  40.  C,  Q  (25). 

£0.  C,  P  (750).  ,41.  C,  P  (8J0). 

£S.  Q  (75),  C.  42.  P,  Q  (2.62|). 

24.  Q,  P  ($1.83J0).  £?.  Q  (8J),  0. 

£5.  Q  (50),  P.  «.  Q  (12|),  P  ($25). 

26.  C,  Q  (6J).  #T.  P  (2^0),  Q. 

27.  C,  P  (.1250).  4^.  C,  P  (*1.08i). 

28.  C  ($65.13),  P.  47.  P,  Q  (116f). 

29.  Q  (75),  P  (250).  48.  Q  (66f),  0. 
SO.  Q,  (62|),  P  ($1.86).  49.  Q,  P  (6±#). 
W.  P  (460),  C  ($16.89).  BO.  Q  (8*),  P. 

NOTE.— To  multiply  by  2.33J,  multiply  by  2  and  by  .33J  separately 
and  add  the  products.  Treat  1.16§,  1.12J,  2.83J,  2.62J,  etc.,  in  a  sin 
ilar  manner. 

Articles  Bought  by  100  (C)  or  1000  (M) 

115.  Q  -5- 100  =  Q  in  hundreds.     (Point  off  two  places.) 
Q  -*- 1000  =  Q  in  thousands.     (Point  off  three  places.) 
P  per  100  x  Q  in  hundreds  =  Cost. 
P  per  1000  x  Q  in  thousands  =  Cost. 

EXAMPLE  1. — Find  the  cost  of  384  laths  at  $.33£  per  0. 

FORMULA  SOLUTION 

PperlOOxQ  384x$.33j 

___       =Cost.  -I55-        fcl.28. 

EXAMPLE  2. — Find  the  cost  of  2415  laths  at  $3.25  per  M. 

FORMULA  SOLUTION 

P  per  1000  x  Q     n  2415  x  $3.25     ,.  „  Q  _ 

-  - 


PRICE,    COST,    AND    QUANTITY  73 

PROBLEMS 
Find  the  cost  of: 

1.  781  brick  at  85  cenbs  per  C. 

2.  2107  feet  pine  at  $18.50  per  M, 

3.  6385  feet  hemlock  at  $14.60  per  M. 

4.  1343  posts  at  $12.25  per  C. 

5.  1560  pineapples  at  $8J  per  C. 

6.  2752  pounds  coal  at  25^  per  C. 

7.  687  feet  oak  at  $32  per  M. 

8.  3250  shingles  at  $3.33£  per  M. 

9.  964  pounds  beef  at  $6.25^  per  C. 
10.  4738  feet  timber  at  $23.50  per  M. 

Articles  Bought  by  the  Ton 

116.  Price  per  ton  -*-  2  =  price  per  1000  pounds. 
Price  per  1000  pounds  x  Q  +  1000  =  Cost. 

EXAMPLE. — Find  the  cost  of  2685  pounds  of  hay  at  $12  per 

ton. 

FORMULA  SOLUTION 

P  per  ton  x  Q  $12x2685 

2  x  1000          C°8t-  2x1000 

PROBLEMS 
Find  the  cost  of: 

1.  6842  pounds  of  coal  at  $5.20  per  ton. 

2.  4975  pounds  steel  at  $33.33£  per  ton. 

3.  2360  pounds  sugar  at  $83£  per  ton. 

4-  15837  pounds  old  iron  at  $6.25  per  ton. 

5.  6974  pounds  salt  at  $5.75  per  ton. 

6.  3798  pounds;  price  per  ton,  $6.90. 

7.  8790  pounds;  price  per  ton,  $12.50. 

8.  350  pounds;  price  per  ton,  $9.60. 

Articles  Bought  by  the  Bushel 

117.  EXAMPLE. — F*nd  the  cost  of  2100  pounds  of  wheat 
at  70  cents  per  bushel  of  60  pounds. 

FORMULA 

pounds  x  P  per  bushel     n  SOLUTION 

pound  per  bushel  S  '     2100  +  60  x  70^  =  $24. 50. 

NOTE. — Use  cancellation. 


74  MODERN    COMMERCIAL   ARITHMETIC 

TABLE    OF   BUSHEL   WEIGHTS 

POUNDS  POUNDS  POUNDS 

Apples 56     Corn  (shelled). . . 56      Potatoes 60 

Barley 48     Corn  (ear) 70      Eye 56 

Beans 60     Flaxseed 56      Timothy  seed, .  .45 

Buckwheat 48     Oats 32      Turnips 56 

Clover  seed 60     Onions 57      Wheat 60 

NOTE. — These  weights  are  used  in  most  of  the  States. 


PROBLEMS 
Find  the  cost  of  a  load  of  : 

1.  Oats,  weighing  2146  pounds,  at  350  per  bushel. 

2.  Potatoes,  weighing  3257  pounds,  at  480  per  bushel. 

3.  Apples,  weighing  2980  pounds,  at  220  per  bushel. 

4.  Turnips,  weighing  3425  pounds,  at  480  per  bushel. 

5.  Barley,  weighing  4160  pounds,  at  360  per  bushel. 

6.  Beans,  weighing  3290  pounds,  at  $1.85  per  bushel. 

7.  Buckwheat,  weighing  1846  pounds,  at  580  per  bushel. 
.  8.  Corn,  weighing  2163  pounds,  at  650  per  bushel. 

9.  Flaxseed,  weighing  3375  pounds,  at  400  per  bushel. 

10.  Onions,  weighing  1956  pounds,  at  400  per  bushel. 

11.  Rye,  weighing  2742  pounds,  at  $2.50  per  bushel. 

12.  Wheat,  weighing  3094  pounds,  at  750  per  bushel. 

IS.  Find  the  total  value  of  the  following  produce:  3  loads 
of  wheat  weighing  3122,  2659,  and  3380  pounds  respectively, 
at  850  per  bushel;  1  load  of  barley,  weighing  2755  pounds,  at 
720  per  bushel;  4 loads  of  potatoes,  weighing  3062,  2587,  3420, 
and  2970  pounds  respectively,  at  420  per  bushel ;  2  loads  of 
beans,  weighing  3160  pounds  each,  at  $2.12-^  per  bushel;  and 
1  load  of  apples,  weighing  2875  pounds,  at  480  per  hundred 
pounds. 

NOTE. — Coal  is  sold  by  the  ton,  and  by  the  bushel  of  80  Ibs. 

14.  Find  the  cost  of  a  load  of  coal,  weighing  2260  pounds, 
at  22  cents  per  bushel  of  80  pounds.  What  is  the  equivalent 
price  per  ton? 


FRACTIONS  75 

15.  Find  the  cost  of  2493  pounds  of  coal  at  $5.75  per  ton. 
What  is  the  equivalent  price  per  bushel? 

16.  A  wagon  loaded  with  potatoes  weighs  4750  pounds,  and 
the  wagon  alone  weighs  1426  pounds.     What  are  the  potatoes 

m  worth  at  33$  per  bushel? 

17.  A  cart  loaded  with  coal  weighs  3492  pounds,  and  the 
cart  weighs  1280  pounds.     Find  the  cost  of  the  coal  at  25$  per 
bushel.     Find  the  equivalent  price  per  ton. 

18.  A  wagon  loaded  with  28  bags  of  wheat  weighs  4960 
pounds,  the  wagon  weighs  1420  pounds,  and  each  bag  weighs  2 
pounds.     Find  the  value  of  the  wheat  at  72$  per  bushel. 

19.  Find  the  cost  of  20  bags  of  beans,  weighing  118  pounds 
each,  at  $1.85  per  bushel. 

20.  What  is  the  cost  of  three  loads  of  turnips,  weighing 
2240,  2875,  and  2680  pounds  respectively,  at  28$  per  bushel? 

21.  How  many  pounds  of  shelled  corn,  at  48$  per  bushel, 
can  be  bought  for  $22.50? 

22.  Find  the  cost  of    a   load   of  drying   apples,  weighing 
3120  pounds,  at  18$  per  bushel. 

23.  A  wagon  loaded  with  onions  weighs  5570  pounds,  the 
wagon  and  crates  weigh  1808  pounds.     Find  the  cost  of  the 
onions  at  45$  per  bushel. 

24.  A  man  bought  a  load  of  oats  for  $21.35.     If  the  oats 
weighed  1952  pounds,  what  price  did  he  pay  per  bushel? 

25.  A  wagon  loaded  with  30  bags  of  beans  weighs  5870 
pounds,  the  wagon  weighs  1842  pounds,  and  each  bag  weighs  2 
pounds.     Find  the  cost  of  the  beans  at  $1.25  per  bushel. 


DENOMINATE  NUMBERS 

DEFINITIONS 

118.  Some  things  are  counted;   as,  dollars,  eggs,  tickets. 
Some  things  are  measured;  as,  time,  area,  volume,  weight. 

119.  When  the  name  of  the  objects  counted  or  measured 
is  used  with  the  expressed  number  (6  apples,  3  feet),  the  num- 
ber is  a  Concrete  dumber. 

120.  A  Unit  of    Measure  is  any  standard  by  which  we 
determine  the  number  or  the  amount  of  anything. 

A  dozen,  a  bushel,  a  pound  are  units  of  measure. 

A  shovelful,  a  boxful,  a  dipperful  are  also  units  of  measure. 

The  dozen,  bushel,  and  pound  are  definite  and  established 
units  of  measure.  The  shovelful  is  not  a  definite  or  established 
unit  of  measure. 

Some  units  of  measure  were  established  by  law  (pound, 
yard,  gallon).  Some  were  established  by  custom  (hour,  dozen, 
degree). 

121.  A  number  whose  unit  of  measure  is  established  by 
law  or  custom  is  a  Denominate  Number. 

122.  A  number  that  expresses  units  of  measure  of  the 
same  kind  is  a  Simple  Denominate  Number  (7  pounds) . 

123.  A  number  that  expresses  units  of  measure  of  similar 
kind  but  of  different  values  is  a  Compound  Denominate  Num- 
ber (7  pounds,  6  ounces). 

MEASURES  OF  EXTENSION 

124.  Extension    means    length,  length  and   breadth,    or 
length,  breadth  and  thickness.     This  leaf  is  a  volume,  or  solid; 
it  has  length,  breadth,  and  thickness.     This  page  is  a  surface; 
it  has  length  and  breadth  only.     The  edge  of  the  page  is  a  line ; 

it  has  length  only. 

76 


DENOMINATE    NUMBERS 


77 


125. 


Linear  Measure 


TABLE 

12    inches  (in.)  =  1  foot.  ft. 

3    feet  =  1  yard.  yd. 

5£  yards  or  16£  feet  =  1  rod.  rd. 

320    rods  =  1  mile.  mi. 

mi.       rd.       yd.         ft.  in. 

1   =  320  =  1760  =  5280  =  63360. 

Scale.—  320,  5|,  3,  12. 

In  measuring  cloth,  the  yard  is  divided  into  quarters. 
Yards  and  quarters  are  sometimes  written  thus:  122  (12f), 
153 


Square  Measure 


26. 


TABLE 

144    square  inches  (sq.  in.)  =  1  square  foot.      sq.  ft. 
9    square  feet  =  1  square  yard.      sq.  yd. 

3()i  square  yards  =  1  square  rod.       sq.  rd. 

160    square  rods  =  1  acre.  A. 

640    acres  =  1  square  mile.      sq.  mi. 

Scale.—  640,  160,  30|,  9,  144. 

A  square  1  in.  on  a  side  is  an  inch  square;  a  square  inch. 
A  square  1  ft.  on  a  side  is  a  foot  square; 
a  square  foot. 

A  square  1  yd.  on  a  side  is  a  yard  square; 
a  square  yard. 

A  square  inch   is  equivalent   to   an   inch 
square. 

A  square  foot  is  equivalent  to  a  foot  square. 
A  square  yard  is  equivalent  to  a  yard  square. 

NOTE.  — The  units  of  square  measure  need  not  be  squares.  A  square 
foot  may  be  either  round  or  oblong.  It  is  called  a  square  foot  because 
it  was  derived  from,  and  is  equivalent  to,  a  foot  square.  A  square  foot 
measures  as  much  as  a  foot  square. 

The  number  of  units  of  square  measure  in  a  surface  is  its 
Area. 


78  MODERN    COMMERCIAL   ARITHMETIC 

127.  Cubic  Measure 

TABLE 

1.728  cubic  inches  (cu.  in.)  =  1  cubic  foot.      cu.  ft. 
27  cubic  feet  =  1  cubic  yard.     cu.  yd. 

128  cubic  feet  =  1  cord.  C. 

Scale.— -27,  1728. 


The  units  of  cubic  measure  are  the 
cubic  inch,  cubic  foot,  and  cubic  yard. 
These  units  need  not  be  cubes. 

A  cubic  inch  is  equivalent  to  a  cube 
an  inch  on  each  edge. 

A  cubic  foot  is  equivalent  to  a  cube 
a  foot  on  each  edge. 
A  cubic  yard  is  equivalent  to  a  cube  a  yard  on  each  edge. 
The  number  of  units  of  cubic  measure  a  solid  contains  is  its 
Solid  Contents  or  Volume. 


3  FT 


128.  Surveyors'  Linear  Measure 

TABLE 

7.92  inches  (in.) 
25  links 

4  rods  or  100  links 
80  chains 

Scale.— SO,  4,  25,  7.92. 


Surveyors'  Square  Measure 

129.  United  States  government  land  when  surveyed  is 
divided  into  townships — tracts  of  land  6  miles  square.  A  town- 
ship is  divided  into  36  equal  squares,  square  miles.  Each 
square  mile  is  called  a  section.  A  section  is  divided  into  half- 
sections,  quarter-sections  and  quarter  quarter-sections* 


DENOMINATE    NUMBEBS 


79 


625  square  links  (sq. 
16  square  rods 
10  square  chains 

640  acres 


TABLE 

1.)  =  1  square  rod.  sq.  rd. 

=  1  square  chain,  sq.  ch. 

=  1  acre.  A. 

=  1  square  mile.  sq.  mi. 


Scale.— GIO,  10,  16,  625. 
MEASURES  OF  CAPACITY 


13O. 


Liquid  Measure 

TABLE 

4  gills  (gi.)  =  1  pint. 


pt. 


2  pints 
4  quarts 
gal. 
1  = 


131. 


=  1  quart.       qt. 
=  1  gallon.      gal. 
qt.     pt.      gi. 
4  =  8  =  32 

Scale.—  4,  2,  4. 

Dry  Measure 


TABLE 

2  pints  (pt.)  =  1  quart.  qt. 
8  quarts  =  1  peck.  pk. 
4  pecks  =  1  bushel,  bu. 

bu.     pk.       qt.         pt. 
1    =    4    =    32    =    64 

Scale.— 4,  8,  2. 


MEASURES  OF  WEIGHT 
Avoirdupois  Weight 

Avoirdupois  weight  is  used  for  ordinary  purposes. 

TABLE 

16  ounces  (oz.)        =1  pound.  Ib. 

100  pounds  =1  hundredweight,  cwt. 

20  hundred-weight=l  ton.  T. 

T.     cwt.       Ib.  oz. 

1  =  20  =  2000  =  32000 

Scale.— 20,  100,  16. 


80 


MODERN    COMMERCIAL    ARITHMETIC 


Troy  Weight 
133*  Troy  weight  is  used  by  jewelers. 


Ib. 
1 


TABLE 

24  grains  (gr.)      =  1  pennyweight,  pwt. 

20  pennyweights  =  1  ounce.  oz. 

12  ounces  =  1  pound.  Ib. 


oz. 

-      12      = 


pwt. 

240     = 


5760 


Scale.— 12,  20,  24. 


Apothecaries'  Weight 
134.  Apothecaries'  weight  is  used  by  druggists. 

TABLE 

20  grains  (gr.)  =  1  scruple,  sc.,  or  9 
3  scruples  =  1  dram.  dr.,  or  3 
8  drams  =  1  ounce.  oz.,  or  5 

12  ounces  =  1  pound.      Ib.,  or  Ib 

Ib.      oz.      dr.       sc.          gr. 
1  =  12  =  96  =  288  =  5760 

Scale.— l^  8,  3,  20. 


MEASURES  OF  TIME 


135. 


TABLE 


60  seconds  (sec.)  =  1  minute.  min. 

60  minutes  =  1  hour.  hr. 

24  hours  =  1  day.  da. 

7  days  =  1  week.  wk. 

365  days  =  1  year.  yr. 

366  days                   =  1  leap  year.  1.  yr. 
100  years                  =  1  century.  cen. 

pr.     mo.      da.        hr.         min. 
1  =  12  -  365  =  8760  =  525600  = 

Soak.— 366,  24,  60,  60. 


sec. 
31536000 


DENOMINATE    NUMBERS  81 

136.  The  earth  rotates  from  west  to  east.     The  Day  meas- 
ures the  time  of  one  complete  rotation  of  the  earth  on  its  axis. 

137.  A  straight  north  and  south  line  passing  through  both 
poles   and   through  any  point  on   the  earth's  surface  is  the 
meridian  of  that  point. 

138.  It  is  noon  at  a  place  when  the  meridian  of  the  place 
is  under  the  direct  rays  of  the  sun. 

139.  A.M.   (ante-meridian)    denotes  the  half -day  before 
noon.       P.M.     (post-meridian)    denotes     the     half-day    after 
noon. 

140.  In  astronomy,  the  day  begins  at  noon;  in  business,  it 
begins  at  midnight. 

141.  The  earth  revolves  around  the  sun  in  equal  periods 
of  time.     The  Year  measures  the  time  of  one  revolution  of  the 
earth  around  the  sun. 

142.  A  year  consists  of  365  da.  5  hr.  48  min.  49.7  sec. 
The  Common  Year  is  365  da.     The  Leap  Year  is  366  days. 

143.  If,  to  make  up  for  the  5  hr.  48  min.  49.7  sec.  dropped 
from  each  common  year,  we  add  one  day  to  each  fourth  year, 
we  would  add  44  min.  41.2  sec.  too  much.     In  100  years  we 
would  add  18  hr.  37  min.  10  sec.  too  much.     If  we  omit  adding 
a  day  every  100  years,  we  would  lose  5  hr.  22  min.  50  sec.     In 
400  years  we  would  lose  21  hr.  31  min.  20  sec.     If,  then,  we 
add  one  day  for  each  400  years,  we  will  gain  2  hr.  28  min.  40 
sec. ;  and  in  4000  years  we  would  gain  24  hr.  46  min.  40  sec. 
So  we  omit  adding  a  day  once  in  4000  years. 

Rule  for  Leap  Year. — Century  years  divisible  by  400,  and 
other  years  divisible  by  four,  are  leap  years,  except  the 
year  4000. 

144.  The  day  added  to  leap  year  becomes   the   29th  of 
February. 

145.  In  business,  30  days  are  usually  considered  a  month, 
and  12  months  a  year. 

146.  The  common  year  contains  52  weeks  and  1  day;  the 
leap  year  52  weeks  and  2  days.     Each  year  begins  one  day  later . 
in  the  week  than  the  preceding  year,  except  the  year  following 
leap  year,  which  begins  two  days  later  in  the  week. 


82 


MODEKN    COMMERCIAL   ARITHMETIC 


147.  Days  in  the  Months. — February  has  28  days,  except 
in  leap  year,  when  it  has  29  days. 

Thirty  days  hath  September, 
April,  June,  and  November; 
All  the  rest  have  thirty -one, 
Excepting  February  alone, 
Which  has  four  and  twenty-four, 
Till  leap  year  gives  it  one  day  more. 

MEASURES  OF  ANGLES  AND  AECS 

148.  A  Circumference  is  the  bounding  line  of  a  circle.    An 
Arc  is  any  part  of  a  circumference. 

149.  sl^  of  any  circumference  is  a  Degree  of  the  circum- 
ference.    If  the  space  about  a  point  be  divided  into  360  equal 

parts  or  angles,  by  straight  lines  meet- 
ing at  the  point,  each  angle   is   an 
jfg^  angle  of  1  degree. 

TABLE 

60  seconds  (")=  1  minute.  (') 

60  minutes      =  1  degree.  (°) 

360  degrees       =  1  circumference,  cir. 

Scale.—  360,  60,  60. 
The  length  of  a  degree  of  longitude  at  the  equator  is  nearly 
70  miles. 

MEASURES  OF  VALUE 
Canada  Money 

150.  The  table  of  the  currency  of  Canada  is  the  same  as 
that  of  the  United  States  (see  p.  66),  although  English  money 
also  is  used. 

English  or  Sterling  Money 

151.  The  unit  of  English  money  is  the  Pound  or  Sovereign. 

TABLE 

4  farthings  (far. )  =  1  penny  (d. )    = 
12  pence  =  1  shilling  (s.)  = 

£0  shillings  =  1  pound  (£)  =  $4. 8665 

Scale.— -20,  12,  4. 


DENOMINATE    NUMBERS  83 


French  Money 

TABLE 

10  centimes  (ct.)  =  1  decime  (dc.)  = 
fO  declines  =  1  franc     (fr.)  = 

153.  German  Money 

TABLE 

100  pfennigs  =  1  mark 


154.  COUNTING 

TABLE 

12  things  =  1  dozen.  doz. 

12  dozen  =  1  gross.  gr. 

12  gross    =  1  great  gross.    Gr.  gr. 

REDUCTION  OF  DENOMINATE  NUMBERS 

155*  The  process  of  changing  a  number  expressed  in  one 
denomination  to  an  equivalent  expressed  in  another  denomina- 
tion is  called  Keduction. 

Change  8  dimes  to  cents;  3  dollars  to  dimes;  3  dollars  and 
8  dimes  to  cents. 

156.  Changing  a  number  from  a  higher  to  a  lower  denom- 
ination is  Eeduction  Descending. 

1.  Change  2  ft.  to  inches;  2  yd.  to  feet;  2  yd  and  2  ft.  to 
inches. 

2.  Change  2  qt.  to  pints;  2  pk.  to  quarts;  2  pk.  2  qt.  to 
pints;  2  bu.  to  pecks;  2  bu.  2  pk.  2  qt.  to  pints. 

3.  Change  4  bu.  3  pk.  to  quarts;  1  pk.  to  pints. 

4.  Change  2  hr.  to  seconds;  2  da.  to  minutes. 
NOTE.-—  Reduction  descending  is  performed  by  multiplication. 

157.  Changing  a  denominate  number  from  a  lower  to  a 
higher  denomination  is  Eeduction  Ascending. 

1.  Change  60  cents  to  dimes;  1200  cents  to  dollars;  50 
dimes  to  dollars;  287  cents  to  dimes  and  cents;  365  cents  to 
dollars,  dimes  and  cents. 


84  MODERN   COMMERCIAL   ARITHMETIC 

2.  Change  36  in.  to  feet;  67  in.  to  feet  and  inches;  98  in. 
to  yards,  feet,  and  inches. 

3.  Change  64  qt.   to   pecks,    then  to  bushels;    42  qt.   to 
bushels,  pecks,  and  quarts;  89  pt.  to  higher  denominations. 

NOTE. — Reduction  ascending  is  performed  by  division. 

158.  Under  several  of  the  denominate  tables  is  a  line  of 
equivalents.     Tell  how  one  equivalent  is  found  from  another, 
the  highest  denomination  from  the  lowest,  the  lowest  from  the 
highest. 

159.  Principles.— 1.  To    perform   reduction   descending, 
multiply  by  the  numbers  in  the  scale  from  the  given  to  the 
required  denomination. 

2.  To  perform  reduction  ascending,  divide  by  the  numbers 
in  the  scale  from  the  given  to  the  required  denomination. 

Model  Solutions 

160.  EXAMPLE  1. — Reduce  12  yd.  2  ft.  9  in.  to  inches. 
OPERATION 

12yd. 
3  ft.  (multiply) 

3®  t  NOTE. — The  product  is  of  the  same  denom- 

2  ft.   (add)  ination  as  the  multiplicand.     The  multiplier 

3g  ft  must  be  an  abstract  number,  so  12  in  the  first 

12  in*  (multiply)        case  an(i  ^  *n  the  second  are  considered  ab- 

stract  numbers  and  the  multipliers. 

456  in. 

9  in.  (add) 

465  in. 

EXAMPLE  2. — Eeduce  892  in.  to  higher  denominations. 

OPERATION 

Divide  12    in.    |  892  in. 
Divide    3    ft.         74  ft.    4  in.  remainder 
Divide    5|  yd.   j     24  yd.   2  ft.  remainder 
4  rd.    2  yd.  remainder 
.-.  892  in.  =  4  rd.  2  yd.  2  ft.  4  in. 
NOTE. — The  divisors  are  considered  abstract  numbers. 


DENOMINATE   NUMBERS  86 

EXAMPLE  3. — Eeduce  f  ft.  to  the  fraction  of  a  rod. 

OPERATION  EXPLANATION.— Divide  |  by  3  and  the 

f  ft.  x  J  x  T2T  =  -fa  ft.         quotient  by  o£. 

EXAMPLE  4. — Eeduce  .8  pt.  to  the  decimal  of  a  bushel. 

OPERATION 

P  '   I  * E_J  EXPLANATION.— Divide  .8  pt.  by  2,  the  quo- 

"  *$•    \   -^ V-          tient  by  8  and  this  quotient  by   4,  as  abstract 

4  pk.  |   .05  pk.         numbers. 

.0125  bu. 

EXAMPLE  5. — Eeduce  £  rd.   to  integers  of  lower  denom- 
inations. 

OPERATION 

i  (rd.)  x  5i  =  2£  yd. 
f  (yd.)  x  3  =  2i  ft. 
|  (ft.)  x  12  =  3  in. 

.-.  ird.  =2  yd.  2ft.  Sin. 

EXAMPLE  6. — Eeduce  .7  bu.  to  integers  of  lower  denomina- 
tions. 

OPERATION 

.7  bu.    (multiplier)  NOTE.— Since  the  decimal  is  to  be 

_  P*F;  reduced  to  integers,  multiply  only  by  the 

2.8  pk.    (multiplier)  decimal  part  of   the  multiplier.      The 

8  qt.  product  is  of  the  same  denomination  as 

6.4  qt.     (multiplier)  the  multiplicand,  but  when  the  product 

2  pt.  is  used  again  as  a  multiplier  it  is  consid- 

~^  pj.  ered  as  an  abstract  number. 

.7  bu.  =2pk.  6  qt.  .8  pt. 

PROBLEMS 
Eeduce  to  higher  denominations: 

1.  4256  in.         8.  12863  sq.  in.  15.  6952  sq.  in. 

2.  86579  in.        9.  6871  sc.  16.  68754  min. 

3.  684  pt.  dry.      10.  9478  1.  17.  61453  gr.  Troy. 
I*.  1272  gi.        -11.  42735  in.  18.  567389  cu.  in. 

5.  1298  gr.  Troy.    12.  6853  gi.       19.  1593  pt.  dry. 

6.  15652  gr.  apoth   -IS.  735  sc.        20.  11268  pwt. 

7.  489754  sec.      14.  627841. 


86 


MODERN    COMMERCIAL   ARITHMETIC 


Reduce  to  the  lowest  denomination  given : 


21.  8  rd.  2  yd.  1  ft.  4  in. 

22.  3  mi.  80  rd.  4  yd.  2  ft. 
28.  2  Ib.  10  oz.  16  gr.  Troy. 

24.  4  hr.  17  min.  40  sec. 

25.  12  Ib.  6  dr.  2  sc. 

26.  16  rd.  12  ft.  7  in. 

27.  17  Ib.  2  pwt. 

28.  2  da.  26  min. 

29.  4  Ib.  7  oz.  1  sc. 
80.  16°  20". 


31.  20°  15'  20". 

£#.  5  gal.  3  qt.  1  pt.  3  gi. 

88.  14.  bu.  3  pk.  5  qt.  1  pt. 

34.  3  cu.  yd.  15  cu.  ft.  806  cu.  in. 

35.  20  gal.  2  qt.  1  pt. 

86.  16  gal.  1  pt.  2  gi. 

87.  2  bu.  2  pk.  1  pt. 

88.  5  cu.  yd.  12  cu.  ft. 

39.  14  gal.  2  qt.  2  gi. 

40.  7  Ib.  3  oz.  2  dr. 


Reduce  to  lower  denominations  : 

41.  frd.  45.   |da. 

42.  J-  mi.  40.   .76  Ib.  apoth. 

43.  .86  rd.  -47.   T\  cu.  yd. 
44-  t  Ib.  Troy.             48.  |  bu. 


-40. 
50. 


.94  gal. 
^  sq.  yd. 
}  gal. 
.55  sq.  rd. 


Reduce  to  a  fraction  of  the  highest  denomination  : 


53.  I  pt.  dry. 

54.  .62  gi. 

55.  I  yd. 

56.  Jdr. 


57.  |  pwt. 

58.  .56  cu.  ft. 

59.  J  1. 

00.  .85  gr.  Troy. 


61.   Jgi. 
00.  i  rd. 
05.   .96  pwt. 
0-4.   .35  dr. 


EXAMPLE  7. — Reduce  2  pk.  6  qt.  1  pt.  to  the  decimal  of  a 

bushel. 

OPERATION 

2  |  1  pt. 

8  |  6.5  qt. 

4|  2.8125pk. 

.703125  bu. 
Or, 

2  pk.  6  qt.  1  pt.  =  45  pt. 
1  bu.  =  64  pt. 

45  pt.  +  64  =  .703125  pt. 


EXPLANATION.  —  Reduce  1  pt.  to 
quarts  and  annex  the  result  to  6  qt. 
Reduce  quarts  to  pecks  and  annex  the 
result  to  2  pk.  Reduce  pecks  to  bushels. 


Reduce  to  decimals  of  the  highest  denomination : 

65.  4  oz.  12  pwt.  16  gr.  68.  12s.  lOd. 

66.  12  hr.  40  min.  30  sec.  69..  2  pk.  6  qt.  1  pt. 

67.  2  qt.  1  pt.  2  gi.  70    14s.  6d.  2  far. 


DENOMINATE    NUMBERS  8? 

REDUCTION   OF   ENGLISH  MONEY 

161.  EXAMPLE. — Reduce  12  sov.  12s.  6d.  to  United  States 
money. 

EXPLANATION.  —  Call   each 
OPERATION  ..... 

12  SOY.  12s.  6d.  =  12.624  sov.          f  llhn«  '°5  °' a  <*™**-  *» 
&   A  Q££-  duce  pence  to  farthings  and 

1   SOV.   =  <s>    4.ODDD  ,,    ,,  ,,     .,  -,,,          « 

10  £CM      &A  Qt*fK      <n?£i   /IQ  cal1  the  result  thousandths  of 

12.624  x  $4.8665  =  $61.43  .         „,,        ,0         .0 

a  sovereign.    Thus,  12  sov.  12s. 

Or,    Is.      =  .05    sov.  6d.  =12  sov.  +  .6  sov.  +  .024 

1  far.  =  .001  sov.  sov.  =  12.624  sov.    §4.8665  X 

12.624  =  $61.43. 

PROBLEMS 
Eeduce  to  United  States  money : 

1.  25  sov.     9s.  lid.  4.  16  sov.  18s.     9d.  2  far. 

2.  81  sov.  16s.  8d.  3  far.  5.   34  sov.  14s.  lOd. 

8.  21  sov.  15s.  7d.  1  far.          6.  13  sov.     7s.  4d.  3  far. 

EXAMPLE. — Reduce  $175  to  equivalents  in  English  money. 

SOLUTION 

$175  -*- $4.8665  =  35. 96  sov. 
35.96  sov.  =  35  sov.  19s.  2d.  1.6  far. 
Eeduce  to  equivalents  in  English  money: 

7.  $152.60.  9.  $792.18.  11.  $6450. 

8.  $586.  10.  $384.50.  12.  $586.25. 

FUNDAMENTAL  OPERATIONS  WITH  DENOMINATE 
NUMBERS 

163.  EXAMPLE  1.—  Add  756,  687,  and  479;  also  7  dollars 
5  dimes  6  cents,  6  dollars  8  dimes  7  cents,  4  dollars  7  dimes 
9  cents. 

OPERATION 

756               $75  dimes     6  cents 
687                 68                7 
479  4     7 9 

1922  $19     2  dimes     2  cents 

NOTE. — Since  the  scale  is  decimal  carry  1  for  every  10  as  in  addi- 
tion of  simple  numbers. 


88  MODERN   COMMERCIAL   ARITHMETIC 

EXAMPLE  2.— Add  4  bu.  2  pk.  7  qt.  1  pt.,  6  bu.  3  pk.  6  qt, 
1  pt.,  and  2  bu.  2  pk.  5  qt.  1  pt. 

OPERATION 

4  bu.  2  pk.  7  qt.  1  pt. 

6          3          6*         1  NOTE. — Carry  according  to  the  scale 

2251  of  ^e  table  used. 


14  bu.  1  pk.  3  qt.  1  pt. 

EXAMPLE  3. — From  7  dollars  4  dimes  6  cents  take  2  dollars 

7  dimes  8  cents. 

OPERATION 

746  $74  dimes     6  cents 

278  27         .8 

468  $46  dimes     8  cents 

NOTE. — Change  from  one  denomination  to  another  according  to 
the  scale  of  the  table  used. 

EXAMPLE  4. — Subtract  3  gal.  3  qt.  0  pt.  3  gi.  from  5  gal. 
2  qt.  0  pt.  3  gi. 

OPERATION 

5  £al    2  at    0  pt    2  gi  NOTE. — Change    from    one  denomina- 

3         0         3  tion  to    another  according   to   the  scale 

1  gal.  2  qt.  1  pt.  3  gi.      used> 

EXAMPLE  5. — Multiply  2  dollars  5  dimes  8  cents  by  7. 

OPERATION 
258  $25  dimes     8  cents 

7  7 


18     0     6  $18     0  dimes     6  cents 

EXAMPLE  6. — Multiply  4  gal.  3  qt.  1  pt.  2  gi.  by  6. 

OPERATION 
4  gal.  3  qt.  1  pt.  2  gi. 

6 

29  gal.  2  qt.  1  pt.  0  gi. 

EXAMPLE  7. — Divide  8  dollars  5  dimes  5  cents  by  3. 

OPERATION 
3)855  3) $8     5  dimes     5  cents 

285  $2     8  dimes     5  cents 


DENOMINATE    KUMBERS 


EXAMPLE  8.-— Divide  5  bu.  1  pk.  7  qt.  by  4. 

OPERATION 
4)5  bu.  1  pk.  7  qt. 


1  bu.  1  pk.  3  qt.  H  pt. 

PROBLEMS 

1.  Add  2  Ib.  6  oz.  16  pwt.  18  gr.,  8  Ib.  11  oz.  17  pwt.  21  gr., 
14  Ib.  9  oz.  12  pwt.  20  gr. 

2.  From  1  mi.    60  rd.   4  yd.   1  ft.  4  in.  take  130  rd.  2  yd. 
2  ft.  9  in. 

8.  Multiply  12  gal.  3  qt.  1  pt.  3  gi.  by  8. 

4.  Add  2  cu.  yd.  16  cu.  ft.  987  cu.  in.,  8  cu.  yd.  20  cu.  ft. 
1265  cu.  in. 

5.  Divide  7  Ib.  10  oz.  12  pwt.  16  gr.  by  4. 

6.  Divide  20  bu.  4  qt.  by  2  bu.  3  pk.  4  qt. 
NOTE. — Reduce  both  expressions  to  quarts,  then  divide. 

7.  Divide  48  gal.  1  qt.  3  gi.  by  3  gal.  2  qt.  1  pt.  3  gi. 

8.  Multiply  6  bu.  3  pk.  5  qt.  by  14. 

9.  From  12  da.   16  hr.   30  miri.  14  sec.  take  9  da.  20  hr. 
50  sec. 

10.  Add  1  mi.  165  rd.  2  yd.  8  in.,  3  mi.  120  rd.  4  yd.  2  ft. 

11.  Divide  12  bu.  3  pk.  7  qt.  into  8  equal  parts. 

12.  How  many  jugs  holding  1  gal.  1  qt.  1  pt.  each  can  be 
filled  from  a  barrel  containing  54  gal.  2  qt.  1  pt. 

18.  Add  3  Ib.  6  oz.  7  dr.  2  sc.   16  gr.,  4  dr.  2  sc.  12  gr., 

1  Ib.  9  oz.  1  sc.  8  gr.,  11  oz.  2  sc.  18  gr.,  1  Ib.  8  oz.  5  dr. 

14.  Multiply  3  da.  12  hr.  30  min.  14  sec.  by  12. 

15.  Subtract  1  mi.   190  rd.  4  yd.  8  in.  from  2  mi.  60  rd. 

2  yd.  2  ft.  9  in. 

16.  How  many  times  is  2  dr.  2  sc.  12  gr.  contained  in  1  Ib. 
2  oz.  5  dr.  1  sc.  12  gr. 

17.  Add  6  gal.  2  qt.  1  pt.  3  gi.,  12  gal.  3  qt.  2  gi.,  17  gal. 

1  qt.  1  pt.  3  gi. 

18.  Multiply  3  mi.  80  rd.  5  yd.  2  ft.  8  in.  by  16. 

19.  Subtract  1  yr.  6  mo.  15  da.  9  hr.  45  min.  28  sec.  from 

2  yr.  3  mo.  12  da.  4  hr.  20  min. 


90  MODERH   COMMERCIAL   ARITHMETIC 

20.  Multiply  6  Ib.  9  oz.  12  pwt.  16  gr.  by  13. 

21.  Add  31  mi.  65  rd.  3  yd.  1  ft.,  196  rd.  2  yd.  2  ft.  9  in., 
3  mi.  145  rd.  5  yd.  1  ft.  8  in.,  7  mi.  98  rd.  4  yd.  2  ft.  10  in. 

22.  Add  60  A.   90  sq.  rd.   20  sq.  yd.   5  sq.  ft.,   12  A.   120 
sq.  rd.  20  sq.  yd.  8  sq.  ft.,  16  A.  80  sq.  rd.  16  sq.  yd.  5  sq.  ft. 

28.  Subtract  3  gal.  3  qt.  1  pt.  2  gi.  from  8  gal.  1  qt.  3  gi. 

24.  Multiply  7  bu.  3  pk.  6  qt.  1  pt.  by  21. 

25.  Add  1  yr.   6  mo.   13  da.   12  hr.  40  min.,  2  yr.  7  mo. 
15  da.   13  hr.   30  min.,  9  mo.   25  da.   17  hr.  48  min.,  8  mo. 
24  da.  14  hr. 

SUBTRACTION   OF  DATES 

163.  EXAMPLE. — Find    the    difference    in  time    between 
April  6,  1900,  and  Nov.  11,  1899. 

OPERATION  EXPLANATION. — Write  the  time  as  years,  months 

yr.  mo.  da.  and  days.  April  is  the  fourth  month  and  is  written 
1900  4  6  as  4  mo.  November  is  the  eleventh  month  and  is 
1899  11  11  written  as  11  mo.  One  month  is  also  called  30  days. 
4  25  As  the  number  of  days  in  a  month  varies,  this 
method,  called  compound  subtraction,  may  not  give 
the  exact  number  of  days'  difference.  Thus,  counting  30  days  to  a 
month,  the  difference  between  the  above  dates  as  shown  in  the  opera- 
tion is  145  days,  but  the  true  difference  is  146  days.  To  find  the  exact 
number  of  days,  count  the  number  of  days  by  months  from  the  first 
date  to  the  second.  Thus,  19  (days  in  November  after  November  11), 
31  (December),  31  (January),  28  (February),  31  (March),  and  6  (days 
counted  in  April)  are  146. 


PROBLEMS 

Find  the  difference  in  time  between  the  following  dates,  by 
compound  subtraction: 

1.  March  4,  1899,  and  Dec.  11,  1901. 

2.  June  21,  1899,  and  April  2,  1903. 
8.  Aug.  30,  1897,  and  May  15,  1899. 

4.  Sept.  26,  1895,  and  Nov.  12,  1897. 

5.  Oct.  20,  1900,  and  Feb.  6,  1904. 


DENOMINATE    NUMBERS  91 


Find  the  actual  difference  in  days  between : 

6.  Jan.  7,  1900,  and  July  12,  1900. 

7.  Oct.  16,  1900,  and  Jan.  17,  1901. 

8.  Dec.  6,  1901,  and  March  14,  1902. 

9.  May  4,  1902,  and  Oct.  30,  1902. 
10.  Sept.  23,  1900,  and  Feb.  26,  1901. 


COMPARISON  OF  WEIGHTS  AND  MEASURES 

164.  TABLE 

TROY  APOTHECARIES'  AVOIRDUPOIS 
1  lb.  =  5760  gr.  =  5760  gr.  =  7000  gr. 
1  oz.  =  480  gr.  =  480  gr.  =  437.5  gr. 

1  bu.  (32  qt.)  =  2150.42  cu.  in. 
1  gal.  =    231        cu.  in. 

1  qt.  (dry)       =      67£     cu.  in. 
1  qt.  (liquid)  =      57|     cu.  in. 
1  cu.  ft.  water  =      62^-     lb.  avoir. 
1  gal.  water     =        8$     lb.  avoir. 

Which  is  heavier,  a  pound  Troy  or  a  pound  avoirdupois?  an 
ounce  Troy  or  an  ounce  avoirdupois?  Which  is  larger,  a  quart 
dry  measure  or  a  quart  liquid  measure? 

NOTE. — Large  fruits,  vegetables,  coal,  etc.,  are  measured  by  the 
heaped  bushel,  or  the  bushel  of  40  quarts. 

PROBLEMS 

1.  How  many  liquid  quarts  in  a  bushel? 

2.  Change  1  lb.  Troy  to  the  fraction  of  a  pound  avoirdupois. 
8.  Change  8  lb.  12  oz.  avoirdupois  to  apothecaries'  weight. 

4.  Change  1  lb.  avoirdupois  to  Troy  integers. 

5.  How  many  prescriptions  of  1  dr.  2  sc.  12  gr.  can  be  filled 
from  14  oz.  avoirdupois? 

6.  A  60  qt.  liquid  measure  is   equivalent  to  what  in    dry 
measure? 


92  MODERK   COMMERCIAL   ARITHMETIC 

7.  A  bin  that  holds  620  bu.  of  wheat  will  hold  how  many 
bushels  of  potatoes? 

8.  A  tank  that  holds  1280  gal.  will  hold  how  many  bushels 
of  wheat? 

9.  Since  1728  cu.  in.  make  1  cu.  ft.,  and  1  gal.  contains  231 
cu.  in.,  how  many  gallons  in  1  cu.  ft.? 

10.  A  cistern  that  contains  384  cu.  ft  will  hold  how  many 
gallons? 

PAPERS   AND   BOOKS 

165.  TABLE 

24  sheets     =  1  quire 
20  quires  or  500  sheets     =  1  ream 
2  reams     =  1  bundle 
5  bundles  =  1  bale 

NOTE. — The  480-sheet  ream  is  now  used  rarely  in  this  country 
except  for  stationery,  and  odd  and  fancy  papers. 

166.  Book  Paper. — The  paper  out  of  which  books,  circu- 
lars, and  pamphlets  are  usually  made  is  called  Book  Paper.     It 
is  sold  in  large  unfolded  sheets. 

167.  Flat,  Linen,  and  Ledger  Papers.— The  paper  out  of 
which  billheads,  letterheads,  blank  books,  writing  books,  etc., 
are  made  is  called  Flat  Paper.     Flat  paper  is  more  expensive 
than  book  paper. 

Both  book  and  flat  papers  come  in  sheets  of  various  sizes. 

168.  SIZES    OF   BOOK    PAPER 

NOTE.— 22  in.  by  32  in.  may  be  written  22"  X  32",  as  in  the  fol- 
lowing table : 

22" x  32"  25" x  38"  28"  x  42"  36"  x  48" 

24"  x  36"  25"  x  40"  32"  x  44"  38"  x  50" 

169.  SIZES    OF   FLAT   PAPER 

14"  x  17"  17"  x  22"  17"  x  28"  18" x  46" 

15" x  19"  16"  x  26"  20"  x  28"  22" x  31" 

16"  x  21"  19"  x  24"  21"  x  32"  23"  x  36" 
18" x  23" 


DENOMINATE    NUMBERS  93 

Paper  Folding 

17O.  This  table  shows  the  number  of  leaves  into  which 
book  paper  is  folded  in  making  books : 

NAME  OF  FOLD  LEAVES  PAGES 

Folio 2  4 

Quarto  (4to) 4  8 

Octavo  (8vo) 8  16 

Duodecimo  (12mo) 12  24 

16mo 16  32 

18mo 18  36 

24mo 24  48 

32mo  .  32  64 


EXERCISE  IN  FOLDING 

1.  Make  a  folio ;  a  quarto. 

2.  An  octavo  may  be  %  the  width  and  ^  the  length,  or  ^  the 
width  and  |-  the  length  of  the  sheet.     Make  both  kinds. 

3.  A  duodecimo  may  be  ^  the  width  and  %  the  length,  or  ^ 
the  width  and  -J-  the  length  of  the  sheet.     Make  both  kinds. 

4.  Make  a  16mo  ^  the  width  and  ^  the  length  of  the  sheet. 

5.  A  24mo  may  be  \  the  width  and  \  the  length,  or  \  the 
width  and  \  the  length,  or  J  the  width  and  £  the  length,  or  £ 
the  length  and  -J-  the  width  of  the  sheet.     Make  a  24mo  of 
each  kind. 

PROBLEMS 

1.  Give  two  possible  sizes  of  the   pages  of   quarto  books 
made  from  paper  (a)   24"  x  36",    (b)  25"  x  38",   (c)  28"  x  42", 
(d)  32"  x  44". 

2.  Give  the  two  sizes  of  the  pages  of  a  12mo  book  made 
from  paper  24"  x  36" 

SOLUTION 

24" -3  =  8"       36"  +  4  =  9"       Page,  8"  x    9" 
Or,  24"  -^4  =  6"       36"  ^  3  =  12"     Page,  6"  x  12" 

3.  Give  the  possible  sizes  of  the  pages  of  a  24mo  book  made 
from  paper  24"  x  36". 


94  MODERN    COMMERCIAL    ARITHMETIC 

SOLUTION 
3x8  =  24         4x6  =  24         2x12  =  24 

24"  +3=8"  36"  +    8  =    4f  Page,  4£"  x    8" 

Or,  24"  +8=3"  36"  +    3  =  12  "  Page,  3  "  x  12" 

Or,  24"  +4=6"  36"  +6=6"  Page,  6  "  x    6" 

Or,  24"  +6=4"  36"  +4=9"  Page,  4  "  x    9" 

Or,  24"  +    2  =  12"  36"  +  12  =    3  "  Page,  3  "  x  12" 

Or,  24"  +  12  =    2"  36"  +    2  =  18  "  Page,  2  "  x  18" 
NOTE. — Pages  3"  X  12"  and  2"  X  18"  would  be  very  rare. 

4.  Find  the  possible  sizes  of  the  pages  of  an  18mo  book 
made  from  paper  28"  x  42" 

5.  What  size  of  page  can  be  made  by  folding  a  sheet  22"  x  28" 
into  an  8vo? 

6.  What  size  of  page  can  be  made  by  folding  a  sheet  22"  x  32" 
into  a  16mo  book? 

7.  What  size  of  page  can  be  made  by  folding  a  sheet  32"  x  44" 
into  a  24mo  book? 

8.  What  size  of  page  can  be  made  by  folding  a  sheet  32"  x  44" 
into  a  32mo  book? 

9.  What  size  of  pages  can  be  printed  from  a  sheet  of  paper 
28"  x  42",  using  the  18mo  form? 

10.  What  size  of  pages  can  be  printed  from  all  the  sheets  in 
the  table  of  book  paper,  using  the  24mo  form? 

11.  What  size  of   billheads  can  be  made  from   flat  paper 
24"  x  38",  using  the  24mo  form? 

12.  Using  the  24mo  form,  what  size  of  flat  paper  should  be 
purchased  to  make  letterheads  o-J-"  x  8J"  with  the  least  waste? 

IS.  A  publisher  wishes  to  print  •  a  16mo  book  4^"  x  6-J-". 
What  size  of  paper  should  he  buy? 

14.  What  size  of  paper  should  be  purchased  to  make  a  24mo 
book  5"  x  7i"? 

15.  What  size  of  book  paper  should  be  bought  to  make  a  12mo 
blank  book  8"  x  11"? 


DENOMINATE    NUMBERS  95 

PRICE,  COST,  AND  MIXED   QUANTITIES 

171.  Merchants  and  manufacturers  often  have   occasion 
to  form  a  compound  or  mixed  substance  by  combining  different 
ingredients  or  similar  ingredients  of  different  qualities.     Thus, 
a  grocer  may  mix  Rio  coffee  with  Java  coffee,  a  confectioner 
may  mix  two  or  more  kinds  of  candy,  and  a  manufacturer  of 
paint  mixes  different  oils,  colors,  and  leads.     In  such  cases  it  is 
necessary  to  find  the  price  per  pound,  quart,  etc.,  of  the  mix- 
ture.    If  the  dealer  wishes  to  make  a  mixture,  to  be  sold  at  a 
certain  price,  it  is  necessary  for  him  to  know  what  quantities  of 
each  ingredient  to  put  into  the  compound  to  make  the  resulting 
mixture  of  the  required  value. 

To  Find  the  Price  of  a  Mixed  Quantity 

172.  EXAMPLE. — A    grocer    mixed    in    equal    quantities 
coffees  worth  120,  150,  and  180  per  pound  respectively.     At 
what  price  per  pound  should  he  sell  the  mixture? 

FORMULA  EXPLANATION. —  The  quantity  is  3 

Cost  (of  mixture)  lb  '  the  cost  is  45^  (12+ 15  + 18)>  and 

^ L  =  frice.      the  price  is  therefore,  45^  -r-  3,  or  15^ 

Quantity  ^  £ 

MENTAL  PROBLEMS 

1.  At  what  price  should  the  mixed  candy  be  sold,  if   in 
making  it,  candies  selling  for  80,  100,  and  150  respectively  are 
mixed  in  equal  quantities? 

2.  Coffee  worth  150  per  pound  is  mixed  in  equal  quantities 
with  coffee  worth  220  per  pound.    What  is  the  value  per  pound 
of  the  mixture? 

3.  100  lb.  of  sugar  worth  6-J-0  per  pound  are  mixed  with 
50  lb.  worth  50  per  pound.     What  is  the  value  of  a  pound  of 
the  mixture? 

NOTE. — If  the  quantities  mixed  have  a  common  divisor,  the  quo- 
tients of  the  common  divisor  may  be  taken  instead  of  the  quantities 
themselves.  Thus,  instead  of  100  lb.  and  50  lb.,  2  lb.  and  1  lb.  may 
be  used. 


96  MODERN"    COMMERCIAL   ARITHMETIC 

4.  20  qt.  of  wine  worth  200  per  quart  are  mixed  with  10 
qt.  of.  cider  worth  50  per  quart.     What  is  the  price  of  the  mix 
ture  per  gallon? 

5.  40  gal.  of  rum  at  $2.25  per  gallon  are  mixed  with  5  gal. 
of  water.     "What  is  the  mixture  worth  per  quart? 

6.  Find  the  price  of  mixed  nuts  if  the  lot  is  made  up  of 
equal  quantities  worth  90,  120,  and  180  respectively. 

7.  100  Ib.  of  tea  worth  250  per  pound  are  mixed  with  75  Ib. 
worth  180  per  pound.     What  is  the  value  of  a  pound  of  the 
mixture? 

8.  10  Ib.  of  pepper  worth  400  per  ounce  are  mixed  with 
15  Ib.  worth  300  per  ounce.     What  is  the  value  of  the  mixture 
per  ounce? 

9.  Beans  worth  $2.15  per  bushel  are  mixed  in  equal  quanti- 
ties with  beans  worth  $2.05  per  bushel.     Find  the  price  per 
quart  of  the  mixed  beans. 

10.  Syrup  worth  450  per  gallon  is  mixed  in  equal  quantities 
with  syrup  worth  750  per  gallon.     Find  the  price  of  the  mix- 
ture per  quart. 

PROBLEMS 

1.  A  paint  dealer  mixed  300  gal.  of  oil  worth  650  per  gallon 
with  250  gal.  worth  87|0  per  gallon,  and  140  gal.  worth  700 
per  gallon.     Find  the  price  of  1  gallon  of  the  mixed  oil. 

2.  A  druggist  made  a  composition  drug  using  ingredients 
of  the  following  weights  and  values:  14  Ib.  9  oz.  at  300  per 
ounce,  9  Ib.  6  oz.  4  dr.  at  280  per  ounce,  21  Ib.  6  oz.  at  250 
per  ounce,  and  7  dr.  2  sc.  at  100  per  dram.    Find  the  price  per 
dram  of  the  mixture. 

3.  A  manufacturer  mixed  1  T.  14  cwt.  of  wool  at  680  per 
pound  with  1  T.  15  cwt.  75  Ib.  at  550  per  pound,  and  960  Ib. 
at  500  per  pound.     What  was  the  value  per  pound  of  the 
mixed  wool? 

4.  A  dealer  mixed  10  bbl.  of  wine  worth  900  per  gallon  with 
8  bbl.  worth  750  per  gallon,  7  bbl.  worth  500  per  gallon,  and 
40  gal.  of  water.     What  was  the  liquor  worth  per  gallon? 

5.  A  patent-medicine    manufacturer  mixed  ingredients  of 
the  following  volumes  and   values:   18  gal.  at  $1.85,  2  gal. 


DENOMINATE   NUMBERS 


97 


water,  1  gal.  at  $3.75,  1  pt.  at  $1.30,  2  gr.  at  200,  and  a  drug 
worth  $2.40  which  added  nothing  to  the  bulk  of  the  liquid.  If 
he  sold  the  mixture  for  twice  what  it  cost  him,  what  was  the 
price  per  pint? 

To  Find  What  Quantities  Must  Be  Used  to  Produce  a  Mixture  of 
a  Given  Price 

173.  EXAMPLE. — A  grocer  wishes  to  sell  mixed  tea  for  250 
per  pound,  and  desires  to  mix  teas  worth  450,  350,  200,  and 
100  per  pound.  What  proportional  quantities  of  each  may 

he  use? 

OPERATION 


1. 

2. 

3. 

4. 

5. 

6. 

7. 

25 

45 
35 

20 
10 

15 

5 

3 

1 

3 
1 

20 
10 

5 
15 

20 

10 

4 

2 

2 
4 

EXPLANATION. — For  convenience,  write  the  required  price  at  the 
left  of  a  vertical  line,  and  the  given  prices  at  the  right.  Write  the 
difference  between  the  given  and  required  prices  in  the  next  vertical 
column  at  the  right.  Thus,  45  —  25  =  20,  35  —  25  =  10,  25  —  20  =  5, 
25  —  10  =  15.  Draw  a  horizontal  line  separating  the  prices  that  are 
greater  than  the  required  price  from  those  that  are  less.  The  numbers 
in  column  2  show  the  number  of  cents  gained  or  lost  by  putting  1  Ib. 
of  tea  at  a  given  price  into  the  mixture,  and  selling  it  at  25^  per 
pound.  Thus,  if  1  Ib.  of  45^  tea  is  sold  for  25^,  20^  is  lost.  If  1  Ib.  of 
10^  tea  is  sold  for  25^,  15^  is  gained,  etc.  The  horizontal  line  separates 
the  gains  from  the  losses.  The  gains  and  losses  must  be  equal.  If  1 
Ib.  of  45^  tea  and  1  Ib.  of  W  tea  be  put  into  the  mixture,  20^  will  be 
lost  on  one,  and  15^  gained  on  the  other.  But  if  15  Ib.  of  the  tea  OQ 
which  20^  is  lost  per  pound  is  mixed  with  20  Ib.  of  the  tea  on  which 
15j^  is  gained  per  pound,  the  gains  and  losses  will  be  equal  (20  X  15 
=  15  X  20).  And  if  5  Ib.  of  the  tea  on  which  10^  is  lost  per  pound 
are  mixed  with  10  Ib.  of  the  tea  on  which  5^  is  gained  per  pound,  the 
gains  and  losses  will  be  equal.  By  comparing  prices,  one  above  and 
one  below  the  horizontal  line,  a  balance  of  gains  and  losses  is  kept, 
and  the  figures  in  columns  3  and  4  show  how  many  pounds  of  each 


98 


MODERN"    COMMERCIAL    ARITHMETIC 


kind  of  tea  may  be  mixed.  The  numbers  in  any  vertical  column  may 
be  multiplied  or  divided  by  any  number,  as  that  will  not  affect  the 
comparative  quantities  of  the  two  substances  mixed.  Reducing  col- 
umns 3  and  4  to  their  simplest  form,  columns  5  and  6  are  obtained. 
These  columns  show  that  3  Ib.  of  the  45^  tea  and  4  Ib.  of  the  W,  1 
Ib.  of  the  35^,  and  2  Ib.  of  the  W  may  be  mixed  and  sold  at  25^  with- 
out gain  or  loss.  This  result  is  shown  in  column  7. 

Suppose  the  prices  given  were  45^,  40^,  35^,  30^,  20^,  10^,  and  the 
required  price  25^.     The  solution  would  be: 


25 

1. 

2. 

i 
3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

11. 

45 

40 
35 
30 

20 
15 
10 
5 

15 

15 

5 

5 

3 

1 

1 

1 

3 

1 
1 
1 

20 
10 

5 

35 

20 

15 

10 

5 

4 

1 

2 

1 

3 
5 

Column  2  shows  the  difference  between  the  given  prices  and  the 
required  price.  By  taking  these  numbers  in  pairs  and  reversing  them^ 
columns  3,  4,  5,  and  6  are  obtained,  which  show  the  comparative  quan- 
tities that  may  be  mixed.  These  columns  are  reduced,  by  dividing 
the  numbers  in  each  by  the  greatest  number  that  will  divide  them,  to 
columns  7,  8,  9,  and  10.  And  the  number  of  pounds  of  each  kind  that 
may  be  used  are  shown  in  column  11.  As  the  numbers  in  any  one  of 
columns  7,  8,  9,  or  10  may  be  multiplied  by  any  number,  an  indefinite 
number  of  changes  may  be  made  in  column  11. 

PROBLEMS 

1.  A  merchant  has  lots  of  pepper  worth  20^,  28^,  35^,  and 
40^  per  pound,  and  wishes  to  form  a  mixture  worth  30^  per 
pound.     How  many  pounds  of  each  may  he  use?     Give  five 
answers.     If  he  uses  50  Ib.  of  the  first,  how  many  pounds  of 
each  of  the  others  must  he  use? 

2.  Syrup  worth  40^,  50^,  65^,  and  70^  per  gallon  is  mixed 
and  sold  at  60^  per  gallon.     What  comparative  quantities  of 
each  are  mixed? 

3.  A  dealer  mixed  wines  worth  $1.25,  $1.10,  90^,  and  water, 
so  that  the  mixture  was  worth  $1  per  gallon.     What  quantities 
of  each  were  used?     Give  three  answers. 


DENOMINATE    NUMBERS  99 

4.  How  many  pounds  of  each  kind  of  candy  worth  60,  80, 
100,  and  150  may  be  mixed  to  form  a  compound  worth  1 20 
per  pound? 

5.  Drugs  worth  450  per  ounce,  600  per  ounce,  and  100  per 
dram  were  mixed  and  sold  at  500  per  ounce.     If  8  Ib.  of  the 
second  were  used,  what  quantities  of  the  others  were  used? 

6.  What  proportional  quantities,  worth  850,  750,  650,  550, 
and  400,   may  be  mixed  with  80  Ib.  worth  500  so  that  the 
mixture  shall  be  worth  700  per  pound? 

7.  Oils  worth  650,   87-^-0,   and  700  were  used  to  form   a 
mixture  worth  750.     What   proportional   quantities   of   each 
were  used? 

8.  Coffees  worth  12^-0,  150,  180,  and  250  per  pound  were 
mixed  and  sold  for  200  per  pound.     What  comparative  quanti- 
ties of  each  were  used? 

9.  A  druggist  mixed  chemicals  worth  200  per  ounce,  $3.30 
per  ounce,  60  per  ounce,  and  80  per  dram.     If  the  compound 
was  worth  450  per  oijnce,  what  quantities  of  each  did  he  use? 

BUSINESS   PROBLEMS 

1.  A  dealer  sold  24800  bu.  wheat  for  4135  sov.   12s.    What 
was  the  price  per  bushel  in  United  States  money? 

2.  A  manufacturer  made  20  gross  of  silver  spoons,  each 
weighing  10  pwt.    16  gr.     How  much  did  the  silver  in  the 
spoons  cost  him  at  900  per  ounce  avoirdupois? 

3.  A  gold  dollar  weighs    25.8   gr.  and  is  -fa  pure    gold. 
A  manufacturer  made,  from  United  States  gold  coin,  750  gold 
chains  18  k.  fine.     If  each  chain  weighed  3  oz.  16  pwt.  18  gr., 
what  was  the  value  of  the  coin  melted  to  make  the  chains? 

NOTE.— Pure  gold  is  said  to  be  24  karats  fine.     Gold  that  contains 
fa  alloy  has  |f  of  pure  gold  and  is  18  karats  (18  k.)  fine. 

4.  How  many  vases,  each  containing  8  oz.  16  pwt.  of  pure 
silver  can  be  made  from  95  Ib.  4  oz.  (Troy)  of  silver? 

5.  Find  the  cost,  at  $1.10  per  cwt,  of  three  loads  of  meal 
weighing  as  follows:  1  T.   7  cwt.   60  Ib.,  2  T.   80  Ib.,  1  T. 
12  cwt.  75  Ib. 


100  MODERN    COMMERCIAL   ARITHMETIC 

6.  What  will  be  the  freight  on  75  bbl.  of  oil,  each  weighing 
450  lb.,  at  $2  per  ton? 

7.  What  will  be  the  freight  on  8765  bu.  of  wheat  (60  lb.  = 
1  bu.)  at  750  per  ton? 

8.  A  druggist  bought   150  lb.    of  drugs,  by   avoirdupois 
weight,  at  $7.50  per  pound,  and  sold  them  at  80  per  scruple. 
What  did  he  gain? 

9.  A  dealer  bought  nuts  at  $2  per  bushel  (32  qt.)  and  sold 
them  at  80  per  qt.  liquid  measure.     Find  his  gain  per  bushel. 

10.  A  grocer  bought  peas  for  $2.40  per  bushel,  and  sold 
them  at  100  per  quart.     What  did  he  gain  per  bushel?     What 
part  of  his  purchase  price  did  he  gain? 

11.  What  will  be  the  cost,  at  300  per  bushel  of  60  lb. ,  of 
5  loads  of  potatoes,  weighing  2472  lb.,   3185  lb.,  2817  lb., 
3025  lb.,  2960  lb.? 

12.  Find  the  cost  of  18  gal.  3  qt.  1  pt.  of  wine,  at  220 
per  quart. 

IS.  A  cask  of  brandy  containing  46  gal.  2  qt.  1  pt.  was 
bought  for  $108  and  sold  at  200  per  gill.  What  was  gained? 

H.  A  grocer  bought  8  bu.  of  beans  by  dry  measure  and 
sold  them  by  the  liquid  quart.  How  many  liquid  quarts  did 
he  gain? 

15.  How  many  feet  of  fence  will  be  required  to  inclose  a 
field  25  ch.  41  1.  long  and  21  ch.  40  1.  wide? 

16.  If  fence  wire  weighs  12  oz.   to   the   rod,  how   many 
pounds  of  wire  will  be  required  to  build  a  fence  around  a  field 
19  ch.  20  1.  long  and  14  ch.  30  1.  wide,  if  the  fence  be  made 
8  wires  high? 

17.  Change  $425   to   equivalents  in   French    money;     to 
equivalents  in  German  money. 

18.  Change  1486  francs  to   equivalents  in  United   States 
money. 

19.  Change  2538  marks  to  equivalents  in  United  States 
money. 

20.  If  pine  is  estimated  to  weigh  3000  lb.  per  M,  and  maple 
4000  lb.  per  M,  how  much  freight  must  be  paid,  at  $1.20  per 
ton,  on  4560  ft.  of  pine  and  5872  ft.  of  maple? 


DENOMINATE    NUMBERS  101 

21.  Find  the  cost  of  1865  ft.  of  lumber  at  $17.60  per  M. 

22.  If  it  requires  31  Ib.  of  coal  per  day  to  heat  a  house, 
how  much  will  it  cost  per  week  to  heat  it,  the  price  of  coal 
being  $5.50;per  ton? 

23.  A  farmer  raised  230  bu.  2  pk.  6  qt.  from  9  bu.  2  pk. 
4  qt.  of  seed.     What  was  the  yield  from  one  bushel  of  seed? 

24.  Change  83  sov.  12s.  8d.  to  United  States  money. 

25.  Find  the  total  cost  of: 

12  Ib.  9  oz.  lard  at  11^  per  pound. 
9  Ib.  6  oz.  steak  at  14^  per  pound. 

7  Ib.  4  oz.  mutton  at  9^  per  Ib. 

8  Ib.  12  oz.  pork  at  10^  per  pound. 

2  gal.  2  qt.  1  pt.  molasses  at  60^  per  gallon. 
7  Ib.  5  oz.  cheese  at  12-J^  per  pound. 
20  ft.  cord  at  8^  per  yard. 
100  pickles  at  10<p  per  dozen. 
122  yd.  cloth  at  250  per  yard. 


PRACTICAL  MEASUREMENTS 

AREA  OF  PLANE  FIGURES 

174.  An  Angle  is  the  difference  in  the  direction  of  two 
lines  that  meet,  and  it  is  not  affected  by  the  length  of  the  lines. 

175.  A  Eight  Angle  is  one  whose  sides  are  perpendicular 
bo  each  other. 

NOTE. — If  two  lines  meet  and  make  two  equal  angles,  the  lines  are 
perpendicular  to  each  other. 

176.  Angles  whose  sides  are  not  perpendicular   to  each 
other  are  Oblique  Angles. 

177.  An  Acute  Angle  is  an  oblique  angle  less  than  a  right 
angle. 

178.  An  Obtuse  Angle  is  an  oblique  angle  greater  than  a 
right  angle. 


RIGHT  ANGLE 


ACUTE  ANGLE 


OBTUSE  ANGLE 


179.  Two  lines  that  remain  the  same  distance  from  each 
other  throughout  their  whole  extent  are  Parallel. 

180.  A  Plane  Figure  is  any  plane,  or  flat,  surface. 

181.  A  plane  figure  having  four  sides  is  a  Quadrilateral. 
A,  B,  C,  and  D  are  quadrilaterals. 


182.  A  quadrilateral  whose  opposite  sides  are  parallel  is  a 
Parallelogram.     A,  B,  and  C  are  parallelograms. 

102 


PRACTICAL   MEASUREMENTS  103 

183.  The  opposite  sides  of  a  parallelogram  are  equal. 

184.  The  Base  of  a  figure  is  any  side  on  which  it  may  be 
supposed  to  rest. 

185.  The  Altitude  of  a  figure  is  the  perpendicular  distance 
from  the  base  to  the  side  opposite. 

186.  A  parallelogram  that  has  right  angles  is  a  Rectangle. 

187.  A  rectangle  that  has  equal  sides  is  a  Square. 
A  and  B  are  rectangles;  A  is  a  square. 

188.  To  Find  the  Area  of  a  Rectangle 

EXPLANATION. — 

Units  in  length,  4. 
Units  in  width,  3. 
Units  in  area,  4  X  3  =  12. 

Principle.  — The  area  of  a  rectangle  is  equal  to  the  product 
of  its  length  and  breadth. 

PROBLEMS 

1.  The  side  of  a  square  is  16  ft.     What  is  its  area  in  square 
yards? 

2.  A  field  is  50  rd.  long  and   35  rd.  wide.      How  many 
acres  does  it  contain? 

3.  How  many  square  rods  in  a  park  12  rd.  by  8  rd.? 

4-  How  many  square  feet  in  a  floor  17  ft.  by  16  ft.  8  in.? 

5.  How  many  square  rods  in  a  lot  188  ft.  by  164  ft.? 

6.  How  many  acres  in  a  field  64  rd.  3  yd.  by  42  rd.  4  yd.? 

7.  How  many  acres  in  a  road  3  rd.  wide  and  1  mi.  long? 

8.  Find  the  number  of  square  feet  in  the  walls,  floor,  and 
ceiling  of  a  room  18  ft.  by  22  ft.  by  9  ft.  . 

9.  Find  the  number  of  square  yards  in  the  walls  of  a  room 
16  ft.  square  and  10  ft.  high. 

10.  At  30^  per  square  yard,  what  will  be  the  cost  of  build- 
ing a  walk  4|-  ft.  wide  and  6  rd.  long? 

11.  The  area  of  a  garden  is  \  A.,  and  its  length  is  7  rd. 
How  wide  is  it? 


104 


MODERN"    COMMERCIAL   ARITHMETIC 


12.  How  many  square  feet  in  the  walls,  floor,  and  ceiling  of 
a  room  21  ft.  square  and  9  ft.  high? 

18.  A  field  85  rd.  wide  contains  100  A.  How  much 
must  be  cut  off  one  end  of  the  field  to  make  a  lot  of  34 £  A? 

1J+.  How  many  square  inches  on  the  entire  surface  of  a  stick 
8"  square  and  12  ft.  long? 

15.  Find  the  number  of  square  yards  of  roofing  required  for 
the  two  sides  of  a  roof  which  is  62  ft.  long  and  the  slant  height 
of  which  is  44  ft. 

Land  Measurements 

189.  The  United  States  government  surveyed  the  land  of 
many  of  the  western  States,  and  these  lands  are  often  described 
by  the  government  survey.  Under  the  United  States  survey  a 
north  and  south  line  was  run  as  a  Principal  Meridian.  Range 
lines  were  run  parallel  to  the  principal  meridian  and  six  miles 
apart.  An  east  and  west  line,  called  a  Base  Line,  was  run 
intersecting  the  principal  meridian  at  right  angles.  Township 
lines  were  run  parallel  to  the  base  line  and  six  miles  apart. 
These  lines  divide  the  land  into  townships  six  miles  square. 

EXPLANATION.— The  diagram  shows  how  these  lines  are  drawn, 
and  how  the  townships  are  numbered  and  described. 

Township  lines  run 
east  and  west. 

Range  lines  run 
north  and  south. 

Ranges  are  num- 
bered east  and  west 
from  the  principal 
meridian. 

Townships  are 
numbered  north  and 
south  from  the  base 
line. 

A  is  described  as 
Township  3  North, 
Range  3  West. 

B  is  described  as 
Township  3  South, 
Range  4  East. 


4 

C 

A 

3 

TO 

5' 

2 

f 

5 

4 

3 

2 

1 

1 

2 

3 

4 

5 

1 

Base 

Lfne 

2 

• 

3 

a. 
»' 

3 

B 

4 

C  is  described  as  Township  4  North,  Range  5  East. 


PRACTICAL   MEASUREMENTS 


105 


The  following  diagram  shows  how  a  township  is  divided  into  36  sec- 
tions, each  a  mile  square,  and  how  they  are  numbered  and  described : 


TABLE 

36  square  miles  =  1  township 
36  sections  =  1  township 
1  section  =640  acres 

1  acre  =160  square  rods 

A  is  described  as  N.  W.  J  of  Section 
7,  Township  — ,  Range  — . 

B  is  described  as  S.  |  of  Section  26, 
Township  — ,  Range  — . 


6 

5 

4 

3 

2 

1 

A 

8 

9 

10 

11 

12 

18 

17 

16 

15 

14 

13 

19 

20 

21 

22 

23 

24 

30 

29 

28 

27 

25 

B 

31 

32 

33 

34 

35 

36 

DIAGRAM  OF  A  TOWNSHIP 

The  following  shows  how  a  section  is  divided  and  described : 


D 

N.W.% 
of 

E 
N.E.^ 

of 

A 

N.  W.K 

N.  W.  % 

C 

S.  %  of 

N.  W.  % 

B 

aw.* 

320  A. 

160  A. 

DIAGRAM  OF  A  SECTION 


Sections  are  divided  into 
half  -  sections,  quarter  -  sec- 
tions, half  quarter-sections, 
and  quarter  quarter  -  sec- 
tions. 

A  is  described  as  E.  &  of 
Section  — ,  Township  — , 
Range  — . 

B  is  the  S.  W.  }  of  Section 
— ,  etc. 

C  is  the  S.  |  of  N.  W.  J  of 
Section  — ,  etc. 

D  is  the  N.  W.  \  of  N.  W. 
J  of  Section  — ,  etc. 

E  is  the  N.  E.  \  of  N.  W. 
J  of  Section  — ,  etc. 


PROBLEMS 

1.  Draw  a  principal  meridian,  base  line,  range  lines,  town- 
ship lines,   and  indicate  Township  7  North,    Kange  5  East; 
Township  6  South,  Eange  4  West. 

2.  Find  the  cost,  at  $27  per  acre,  of  the  N.  -£  of  S.  W.  ±  ot 
Section  21,  Township  7  N.,  Range  14  W. 


106  MODERN    COMMERCIAL    ARITHMETIC 

3.  What  is  the  value,   at  $62.50  per  acre,  of  the  S.  £  of 
M".  E.  i  of  Section  25,  Township  38  N.,  Range  13  E.? 

4.  What  is  the  value  of  the  S.  E.  J  of  S.  E.  £  of  Section 
16,  Township  30  S.,  Eange  14  W.,  at  $51.30  per  acre? 

5.  Find  the  cost,  at  $17.50  per  acre,  of  the  S.  |  of  N.  E. 
i  of  Section  3,  Township  9  S.,  Range  4  E. 

6.  Find  the  value,  at  $33£  per  acre,  of  the  E.  -J-  of  Section 
28,  Township  11  IS".,  Range  14  E. 

7.  What  will  be  the  cost  of  the  N.  \  of  the  N.  E.  i  of  Sec- 
tion 2,  Township  8  S.,  Range  21  E.  at  $33^  per  acre  V 

8.  If  the  N".  \  of  S.  E.  \  of  Section  17,  Township  14  N".» 
Range  12  W.,  was  sold  for  $1440,  what  was  the  price  per  acre? 

To  Find  the  Area  of  a  Parallelogram 

19O.  How  does  ABE  compare  in  area  with  D  C  F  ?  How 
does  the  parallelogram  A  B  C  D  compare  in  area  with  the  rectan- 

gle  E  B  C  F  ?  How  does  the 
base  of  the  parallelogram 
compare  in  length  with  the 
base  of  the  rectangle?  How 
does  the  altitude  of  one 
compare  with  that  of  the 
other? 

Principle. — The  area  of  a  parallelogram  is  equal  to  the 
product  of  its  base  and  altitude. 

PROBLEMS 

1.  Find  the  area  of  a  parallelogram  whose  base  is  16  rd. 
and  whose  altitude  is  8  rd. 

2.  What  is  the  area  of  a  field  in  the  form  of  a  parallelogram 
if  its  base  is  53  ch.  31  1.,  and  the  perpendicular  distance  from 
the  base  to  the  side  opposite  is  28  ch.  40  1.? 

S.  The  area  of  a  parallelogram  is  684  sq.  yd.,  and  its  base 
is  36  yd.  Find  its  altitude. 

4.  A  field  in  the  form  of  a  parallelogram  has  a  base  of  68 
rd.  and  an  altitude  of  36  rd.  Find  the  value  of  the  field  at 
$60  per  acre? 


E 


PRACTICAL    MEASUREMENTS 


107 


5.  The  area  of  a  parallelogram  is  3240  sq.  ft.     If  its  alti- 
tude is  51  ft.,  what  is  its  length? 

6.  How  many  square  feet  in  the  ceiling  of  a  room  in  the 
form  of  a  parallelogram  32  ft.  long  and  17  ft.  wide? 

7.  The  opposite  sides  of  a  park  are  parallel,  the  adjacent 
sides  being  24  rd.  and  17  rd.     If  the  distance  between  the  sides 
is  14  rd.,  how  many  square  yards  does  the  park  contain? 

8.  A  parallelogram  is  32  ft.  long,  18  ft.  wide,  and  the  dis- 
tance between  its  ends  is  29  ft.     How  many  square  yards  does 
it  contain? 

9.  A  field  in  the  form  of  a  parallelogram  contains  20  A. 
If  it  is  83  rd.  long,  how  wide  is  it? 

10.  The  base  of  a  parallelogram  is  52  ft.  and  the  altitude  is 
22  ft.     What  is  its  area? 

To  Find  the  Area  of  a  Triangle 
191.  A  plane  figure  having  three  sides  is  a  Triangle. 


Base 


Base 


192.  The  perpendicular  distance  from  the  angle  opposite 
the  base  to  the  base,  or  the  base  extended,  is  the  Altitude 


How  does  triangle  A  compare  in  area  with  triangle  B  ? 

How  does  C  compare  in  area  with  D  ? 

Principles. — 1.  The  diagonal  of  a  parallelogram  divides  it 
into  two  equal  triangles. 

2.  The  area  of  a  triangle  is  equal  to  half  the  product  of  its 
base  and  altitude. 


108  MODERN   COMMERCIAL   ARITHMETIC 

PROBLEMS 

Draw  and  find  the  area  of  triangles  of  these  dimensions: 

1.  Base  64  ft.,  altitude  36  ft. 

2.  Base  120  yd.,  altitude  53  yd. 

3.  Altitude  74  rd.,  base  62  rd. 
4>  Altitude  130  rd.,  base  115  rd. 

5.  Base  86  ft.,  altitude  74  ft. 

6.  Altitude  126  yd.,  base  245  yd. 

7.  How  many  square  yards  in  a  triangular  park  whose  alti- 
tude is  362  ft.  and  base  581  ft.? 

8.  The  area  of  a  triangle  is  65  sq.  yd.  and  its  altitude  is 
18  ft.     Find  its  base. 

9.  Find  the  area  of  the  four  sides  of  a  square  pyramid. 
Each  side  is  40  yards  at  the  base,  and  the  distance  from  the  mid- 
dle of  the  edge  of  the  base  to  the  vertex  is  80  ft. 

10.  How  many  feet  of  lumber  will  be  required  to  cover  a 
triangular  floor  whose  base  is  45  ft.  and  altitude  37  ft.? 

11.  Find  the  area  of  a  triangular  field  if  one  of  its  sides  is 
124  rd.  and  the  distance  from  this  side  to  the  vertex  opposite 
is  56  rd. 

12.  I  wish  to  lay  out  a  triangular  park  that  will  contain 
3  A.     If  I  make  the  base  36  rd.,  how  far  opposite  must  the 
apex  be  placed? 

13.  The  base  of  a  triangle  is  17  ft.  and  the  area  is  75  sq.  ft. 
What  is  its  altitude? 

14-  The  three  sides  of  a  triangle  are  6,  8,  and  10  rd.  If  the 
area  is  24  sq.  rd. ,  what  is  the  distance  of  each  side  from  the 
apex  opposite? 

15.  Find  the  area  of  a  triangle  if  the  altitude  is  14  rd.  and 
the  base  is  29  rd. 

To  Find  the  Area  of  a  Trapezoid 

193.  A  quadrilateral  having  two  sides  parallel  is  a  Trape- 
zoid. 

A  diagonal  of  a  trapezoid  divides  it  into  two  triangles  having 
the  same  altitude. 


PRACTICAL   MEASUREMENTS  109 

EXPLANATION. — 

Area  of  triangle  A  B  C  =  J  of 
B  C  X  alt.  of  the  trapezoid. 

Area  of  triangle  A  C  D  =  J  of  / 

A  D  X  alt.  of  the  trapezoid. 

Area  of  trapezoid  A  B  C  D  =  \ 
of    (AD  +  BC)  X    alt.    of    the      A 
trapezoid. 

Principle. — The  area  of  a  trapezoid  is  equal  to  one-half  of 
the  product  of  the  sum  of  the  parallel  sides  by  the  altitude. 


PROBLEMS 

Draw   and  find  the  area  of  trapezoids    of    the  following 
dimensions: 

1.  Parallel  sides  22  ft.  and  16  ft.,  altitude  14  ft. 

2.  Parallel  sides  36  yd.  and  24  yd.,  altitude  25  yd. 

3.  Parallel  sides  128  rd.  and  75  rd.,  altitude  37  rd. 

4.  Altitude  246  ft.,  parallel  sides  426  ft.  and  538  ft. 

5.  Altitude  42  rd.,  parallel  sides  85  rd.  and  96  rd. 

6.  The  area  of  a  trapezoid  is  4  acres.     The  sum  of  the 
parallel  sides  is  64  rd.     What  is  the  altitude? 

7.  How  many  acres  in  a  field  in  the  form  of  a  trapezoid 
whose  altitude  is  38  rd.  and  whose  parallel  sides  are  56  rd.  and 
62  rd.? 

8.  Find  the  arsa  of  a  park  in  the  form  of  a  trapezoid,  60  rd. 
long,  8  rd.  wide  at  one  end  and  12  rd.  at  the  other. 

9.  One  side  of  a  lot  is  16  rd.  long,  the  side  parallel  to  it  is 
12  rd.  long,  and  the  perpendicular  distance  between  them  is 
8  rd.     How  much  is  the  lot  worth  at  $2  per  square  yard? 

10.  The  area  of  a  trapezoid  is  4  A.     If  the  altitude  is  18 
rd.,  what  is  the  sum  of  the  parallel  sides? 

11.  The  parallel  sides  of  a  field  are  46  rd.  and  28  rd.,  and 
the  distance  between  them  is  26  rd.     What  is  the  area? 

12.  How  many  square  feet  in  a  board  18  ft.  long,  24"  wide 
at  one  end,  14"  at  the  other? 

18.  How  many  square  feet  in  the  two  gable  ends  of  a  house 
32  ft.  wide,  if  the  peak  of  the  roof  is  12  ft.  above  the  plate? 


110  MODERN    COMMERCIAL   ARITHMETIC 

14-  How  many  square  inches  in  a  sheet  of  metal  having  two 
parallel  sides  20"  and  32"  long,  if  the  distance  between  them 
is  19"? 

To  Find  the  Area  of  a  Regular  Polygon 

194.  A  plane  figure  whose  sides  and  angles  are  respectively 
equal  each  to  each  is  a  Kegular  Polygon. 


HEXAGON  OCTAGON 

(AC,  apothem;  AB,  radius.) 

195.  The  Perimeter  of  a  polygon  is  the  sum  of  all  its 
sides. 

196.  The  Radius  of  a  regular  polygon  is  the  distance  from 
the  center  to  any  vertex. 

197.  The  Apothem  of  a  polygon  is  the  perpendicular  dis- 
tance from  the  center  to  any  side. 

198.  The  radii  of  a  regular  polygon  divide  it  into  equal 
triangles.     The  apothem  of  the  polygon  is  then  the  altitude 
of  each  of  these  triangles.     The  perimeter  of  the  polygon  is  the 
sum  of  the  bases  of  the  triangles.     Therefore,  the  area  of  a 
regular  polygon  is  equal  to  one-half  the  product  of  its  perim- 
eter and  apothem. 

Principle. — The  area  of  a  regular  polygon  is  equal  to  one- 
half  the  product  of  its  perimeter  and  apothem. 

PROBLEMS 

1.  Find  the  area  of  a  regular  hexagon  whose  sides  are  5  ft. 
and  whose  apothem  is  4  ft.  4  in. 

2.  The  perimeter  of  a  regular  octagon  is  48  ft.,  and  the 
perpendicular  distance  from  the  center  to  one  side  is  7  ft.  3  in. 
What  is  the  area  of  the  octagon? 


PKACTICAL   MEASUREMENTS  111 

3.  The  side  of  a  regular  pentagon  is  10  yd.  and  the  apothem 
is  7  yd.  1  ft.  5  in.  What  is  the  area? 

4-  The  apothem  of  a  regular  octagon  is  12  ft.  and  each 
side  is  9.94  ft.  What  is  the  area? 

5.  Find  the  area  of  a  regular  hexagon,  if  the  perimeter  is 
36  ft.  and  the  apothem  is  5|  ft. 

6.  Find  the  area  of  a  regular  hexagon  each  of  whose  sides 
is  8"  and  whose  apothem  is  6.93". 

7.  If  the  area  of  a  regular  octagon  is  174  sq.  ft.  and  the 
length  of  one  side  is  6  ft.,  what  is  its  apothem? 

8.  If  the  area  of  a  regular  hexagon  is  374.4  sq.  ft.  and  the 
length  of  one  side  is  12  ft.,  what  is  the  apothem? 

NOTE. — To  find  the  area  of  any  regular  polygon,  multiply  the 
square  of  its  side  by  its  number  in  the  following  table: 

Triangle 433013  Nonagon 6.181824 

Pentagon 1.720477  Decagon 7694209 

Hexagon 2.578076  Dodecagon 11.196152 

Octagon 4828427 

9.  Find  the  area  of  a  regular  pentagon  whose  perimeter  is 
40ft. 

10.  Find  the  area  of  a  regular  decagon  one  of  whose  sides 
is  15  yd. 

11.  If  a  triangle  is  7  ft.  on  a  side,  what  is  its  area? 

12.  If  the  side  of  a  regular  dodecagon  is  15  ft.,  what  is  its 
area? 

13.  Find  the  area  of  a  regular  nonagon  whose  sides  are 
each  22  ft. 

H.  The  side  of  a  regular  pentagon  is  44  yd.  What  is  its 
area? 

15.  What  is  the  area  of  the  floor  of  an  octagonal  room  16  ft. 
on  a  side? 

To  Find  the  Circumference  and  Diameter  of  a  Circle 

199.  A  plane  figure  bounded  by  a  uniformly  curved  line  is 
a  Circle. 

3OO.  The  line  that  bounds  a  circle  is  its  Circumference. 


112  MODERN   COMMERCIAL   ARITHMETIC 

201.  Every  point  in  the  circumference  is  equally  distant 
from  the  center. 

202.  A  straight  line  from  the  center  to  the  circumference 
is  the  Kadius. 

203.  A  straight  line  from  one  side  of  a  circle  through  the 
center  to  the  opposite  side  is  the  Diameter. 

Principles. — 1.  Circumference  =  diameter  x  3.1416. 

2.  Diameter  =  circumference  +  3.1416. 

For  ordinary  purposes,  circumference  =  diameter  x  3^. 


PROBLEMS 

1.  What  is  the  circumference  of  a  circle  whose  diameter 
is  28  ft.? 

2.  Find  the  diameter  if  the  circumference  is  49  yd. 
8.  Find  the  diameter  if  the  circumference  is  56  yd. 

4.  The  radius  is  7  ft. ;  find  the  circumference. 

5.  The  circumference  is  68  yd. ;  find  the  radius. 

6.  The  diameter  is  42  ft. ;  find  the  circumference. 

7.  The  circumference  is  95  yd. ;  find  the  radius. 

8.  The  radius  is  7  rd. ;  find  the  circumference. 

9.  The  circumference  is  123  rd. ;  find  the  diameter. 
10.  The  radius  is  11  ft.  7";  find  the  circumference. 

To  Find  the  Area  of  a  Circle 

2O4.  If  the  number  of  sides  of  a  regular  polygon  be  suffi- 
ciently increased,  the  polygon  will  become  a  circle,  the  perimeter 
will  become  the  circumference,  and  the  apothem  will  become 
the  radius  of  the  circle. 

Principle. — The  area  of  a  circle  is  equal  to  one-half  the 
product  of  its  circumference  and  radius. 

circumference  x  radius 

Area  = 

2 


PRACTICAL   MEASUREMENTS  113 

205.  Inscribe  a  circle  within  a  square.      How  does  the 
'diameter  of  the  circle  compare  in  length  with  a  side  of  the 
square?      How   does   the    circumference    of 

the  circle  compare  in  length  with  4  times 
the  length  of  the  side  of  the  square?  It  is 
just  how  many  times  the  side  of  the  square — 
or  the  diameter  of  the  circle?  How  does  the 
circle  compare  in  area  with  the  area  of  the 
square  around  the  circle?  If  the  side  of 
the  square  is  10  ft.,  what  is  the  area  of  the  square?  What  is 
the  diameter  of  the  inscribed  circle?  What  is  ^  the  circum- 
ference? What  is  the  radius?  What  is  the  area? 

PROBLEMS 

Find  the  area  of  circles  of  the  following  dimensions : 

1.  Circumference  50  ft.,  diameter  15.915  ft. 

2.  Circumference  1  mi.,  diameter  101.856  rd. 

3.  Circumference  60  ft.  8.  Diameter  85  ft. 
4-  Radius  28  in.  9.  Diameter  18  rd. 
,5.  Radius  4  ft.                              10.  Diameter  24  ft. 
'6.   Circumference  26  yd.              11.  Radius  12  rd. 
7.  Circumference  34  yd.              12.  Radius  16  yd. 

13.  How  many  acres  in  a  circular  park  60  rd.  in  diameter? 
H.  How  many  acres  in  a  race-course  1  mi.  in  circumference? 

15.  How  many  square  feet  in  the  bottom  of  a  cistern  6J  ft. 
In  diameter? 

16.  Find  the  area  of  the  side  and  bottom  of  a  cistern,  if  it 
is  6  ft.  deep  and  20  ft.  in  circumference. 

17.  Find  the  entire  surface  of  a  cylinder  8"  in  diameter  and 
18"  long. 

18.  How  many  square  feet  in  a  rug  35  ft.  in  circumference? 

Measurements  by  the  Square  Yard 

206.  The  cost  of  plastering,  ceiling,  painting,  and  paving 
is  usually  computed  by  the  square  yard. 

It  is  customary  to  allow  for  one-half  of  the  area  of  open- 
ings, as  for  doors  and  windows. 


114  MODERN    COMMERCIAL   ARITHMETIC 

PROBLEMS 

1.  Find  the  cost  of  plastering  the  four  walls  of  a  room  16  ft. 
square  and  9  ft.  high,  at  200  per  square  yard. 

2.  How  many  square  yards  in  the  ceiling  of  a  room  22  ft. 
by  18  ft.? 

3.  The  walls  of  a  room  20  ft.  by  18  ft.  and  10  ft.  high  have 
3  ft.  of  wainscoting  and  7  ft.  of  plaster.     Find  the  number  of 
square  yards  in  the  floor,  ceiling,  and  wainscoting,   and  the 
number  of  square  yards  of  plaster  on  the  walls. 

4.  A   room    18   ft.    square   and   10   ft.    high   has   3  doors 
each  3  ft.  by  7J  ft.,  and  4  windows  each  3  ft.  by  6  ft.     How 
many  square  yards  in  the  walls  and  ceiling,  making  one-half 
allowance  for  doors  and  windows? 

5.  Find  the  cost  of  ceiling,  at  200  per  square  yard,  5  rooms 
of  the  following  dimensions:    12  ft.  by  14  ft.,  18  ft.  by  21  ft., 
13  ft.  by  16  ft.,  14  ft.  square,  and  15  ft.  by  18  ft. 

6.  Find  the  cost  of  paying  a  walk  4-^  ft.  wide,  8  rd.  long,  at 
600  per  square  yard. 

7.  How  many  square  yards  of  paying  in  a  street  85  ft.  wide 
and  60  rd.  long? 

8.  How  many  brick  8  in.  by  4  in.  will  be  required,  if  laid 
flat,  to  pave  a  walk  4  ft.  8  in.  wide  and  25  ft.  4  in.  long? 

9.  A  block  of  buildings  measures  320  ft.  by  420  ft.     How 
many  square  yards  in  an  8  ft.  walk  surrounding  the  block? 

10.  How  many  square  yards  of  paving  in  a  courtyard  in  the 
form  of  a  trapezoid,  the  parallel  sides  being  98  ft.  and  76  ft. 
respectively,  and  the  distance  between  these  sides  being  48  ft.? 

11.  Find  the  cost  of  plastering  a  circular  cistern  8  ft.  in 
diameter  and  6  ft.  deep,  at  300  per  square  yard. 

12.  How  many  square  yards  of  plastering  on  a  cistern  7  ft. 
deep,  10  ft.  long,  and  8  ft.  wide? 

13.  A  room  20  ft.  square  and  9  ft.  high  has  8  windows  4  ft. 
by  8  ft.,  and  7  doors  3  ft.  by  8  ft.     How  many  square  yards  in 
the  walls,   ceiling,  and  floor,   allowing  %  space  for  doors  and 
windows? 


PEACTICAL   MEASUKEMENTS  115 

14.  Find  the  cost,  at  28^  per  square  yard,  of  ceiling  the 
sides  and  overhead  of  6  rooms  of  the  following  dimensions :  16 
ft.  by  18  ft.,  12  ft.  by  13  ft.,  9  ft.  by  12  ft.,  8  ft.  by  14  ft.,  13 
ft.  by  14  ft.,  and  11  ft.  square,  each  being  9  ft.  high. 

15.  Find  the  cost  of  paving,  at  75^  per  square  yard,  a 
hexagonal  court  150  ft.  on  a  side. 

16.  How  many  square  feet  of  cement  in  a  circular  court  62 
ft.  in  diameter? 

17.  How  many  square  yards  of  painting  on  the  outside  of  a 
house  50  ft.  long,  32  ft.  wide,  and  21  ft.  high?     The  gable  ends 
are  14  ft.  high,  the  cornice  is  estimated  at  40  sq.  yds.  and  no 
allowance  is  made  for  windows. 

18.  How  many  squares  of  painting,  100  ft.  to  the  square, 
on  the  outside  of  a  brick  chimney  the  slant  height  of  which  is 
60  ft.,  12  ft.  square  at  the  bottom,  and  6  ft.  at  the  top  ? 

19.  How  many  square  yards  of  plastering  on  the  inside  of 
the  above  chimney  if  the  walls  are  1|  ft.  thick? 

20.  How  many  square  feet  of  painting  on  12  stairs,  each 
haying  20  steps  3  ft.  wide  with  a  tread  of  9"  and  a  rise  of  8"? 

Papering 

207.  A  roll  of  wall  paper  is  usually  8  yd.  long  and  18  in. 
wide.     Double  rolls  are  counted  as  two  rolls. 

208.  To  find  the  number  of  rolls  of  paper  required  to  paper 
a  room : 

1.  Find  the  number  of  strips  of  paper  required. 

2.  Find  the  number  of  strips  that  can  be  cut  from  a  roll. 

3.  Divide  the  number  of  strips  required  by  the  number  that 
can  be  cut  from  a  roll. 

NOTE.— Sometimes  waste  occurs  in  matching,  so  that  it  may  not 
always  be  possible  to  estimate  the  exact  number  of  rolls  required. 

PROBLEMS 

1.  How  many  rolls  of  paper,  8  yd.  long  and  18  in.  wide,  will 
be  required  to  cover  the  walls  of  a  room  20  ft.  square  and  9  ft. 
high,  making  allowances  for  6  windows  3  ft.  wide,  and  4  doors 
3£  ft.  wide? 


116  MODERN"    COMMERCIAL   ARITHMETIC 

2.  How  many  rolls  of  paper  will  be  necessary  for  a  room 
22  ft.  long,  15  ft.  wide,  and  8£  ft.  high,  allowing  only  for  4 
doors  3|-  ft.  wide? 

3.  How  many  rolls  of  paper  must  be  used  to  cover  the  ceil- 
ing of  a  room  16  ft.  by  21  ft.,  if  the  paper  runs  crosswise  with 
the  room? 

4.  Find  the  number  of  rolls  of  paper  required  to  cover  the 
walls  and  ceiling  of  a  room  18  ft.  square  and  10  ft.  high.     A 
roll  will  make  two  strips  for  the  wall.     In  the  middle  of  each 
side  is  a  door  3J  ft.  wide,  and  on  each  side  of  each  door  and 
2£  ft.  from  it,  is  a  window  3  ft.  wide. 

5.  How  much  paper  will  be  required  for  the  walls  and  ceil- 
ing of  a  room  12  ft.  by  13  ft.  and  8  ft.  high?     Allow  for  2  doors 
and  4  windows  each  3^-  ft.  wide  and  no  waste  in  matching. 

6.  How  many  yards  of  plain  paper  30"  wide  must  be  used  to 
cover  the  walls  of  a  room  32  ft.  by  28  ft.,  and  14  ft.  high, 
allowing  1  ft.  for  border,  3  ft.  for  wainscoting,  and  for  4  doors 
each  4  ft.  wide,  and  8  windows  each  3-J-  ft.  wide? 

7.  How  many  yards  of  plain  paper  3  ft.  wide  will  be  neces- 
sary to  cover  the  walls  and  ceiling  of  a  hall  120  ft.  long,  12  ft. 
wide,  and  13  ft.  high? 

8.  How  many  rolls  of  paper  will  be  used  for  the  walls  and 
ceiling  of  a  room  17  ft.  by  23  ft.  and  10  ft.  high,  allowing  1  ft. 
for  border,  2  ft.  of  paper  on  each  strip  for  matching,  and  for  5 
doors  and  6  windows,  each  4  ft.  wide? 

Carpeting 

2O9.  Carpets  are  usually  either  1  yd.  or  f  yd.  in  width. 

Allowance  must  be  made  for  waste  in  matching  the  patterns 
in  carpets. 

As  carpets  are  sold  in  strips  and  matched  by  strips,  the 
number  of  strips  required  to  cover  the  floor  must  be  found. 
Sometimes  it  is  necessary  to  cut  off  or  turn  under  part  of  a 
strip,  and  the  part  cut  off  or  turned  under  must  be  included  in 
the  estimate. 

Sometimes  there  is  less  waste  when  the  strips  run  one  way 
in  the  room  than  when  they  run  the  other  way. 


PRACTICAL   MEASUREMENTS  117 

In  finding  the  length  of  border  to  be  put  around  a  carpet 
the  entire  distance  around  the  room  must  be  taken,  as  there  is 
a  waste  at  each  corner  in  making  the  border. 

PROBLEMS 

1.  A  floor  21  ft.  by  24  ft.  is  covered  with  carpet  1  yd.  wide, 
without  waste  in  matching.     Find  the  cost  of  the  carpet  at 
$1.10  per  running  yard. 

2.  If  the  above  room  is  covered  with  carpet  f  yd.  wide, 
what  will  it  cost  at  90^  per  yard? 

3.  Find  the  cost  of  carpeting  a  room  20  ft.  by  27  ft.,  with 
carpet  f  yd.  wide,  at  80^  per  yard,  if  the  strips  run  length- 
wise ;  if  the  strips  run  crosswise. 

4.  How  many  yards  of  carpet  1  yd.  wide  will  be  required 
for  a  room  24  ft.  by  16  ft.,  if  the  strips  run  lengthwise  and  J 
of  a  yard  in  each  strip  is  wasted  in  matching? 

5.  Find  the  least  number  of  yards  of  carpet  required  to 
cover  floors  of  the  following  dimensions,  and  tell  which  way  the 
strips  should  run,  allowing  no  waste  for  matching: 

ROOM  WIDTH  OF  CARPET 
40  ft.  by  42  ft.  1  yd. 

22  ft.  by  15  ft.  f  yd. 

27  ft.  by  34  ft.  f  yd. 

13  ft.  by  15  ft.  1  yd 

14  ft.  by  18  ft.  f  yd. 

6.  Find  how  much  more  carpet  would  be  required  in  each 
case  if  it  were  laid  in  the  opposite  direction. 

7.  Find  the  least  number  of  yards  of  carpet  necessary  to 
cover  floors  of  the  following  dimensions,  allowing  no  waste  for 
matching : 

ROOM  WIDTH  OF  CARPET 
14    ft.  by  22  ft.  1  yd. 

21    ft.  by  24  ft.  f  yd. 

13    ft.  by  17  ft.  1  yd. 

12£ft.  by  16  ft.  f  yd. 

22  ft.  by  25  ft.  f  yd. 


118  MODERN    COMMERCIAL    ARITHMETIC 

MEASUREMENT   OF   SOLID   FIGURES 

To  Find  the  Volume  of  a  Prism 

210.  A  solid  has  length,  breadth,  and  thickness. 

211.  A  solid  that  has  two  parallel  equal  bases,  and  three  or 
more  sides  that  are  parallelograms,  is  a  Prism. 


TRIANGULAR  PRISM 


RECTANGULAR  PRISM 


212.  The  area  of  a  rectangle  is  equal  to  the  product  of  its 
length  and  breadth. 

213.  A  rectangular  prism  that  is  one  unit  high  has  a  vol- 
ume equal  to  the  product  of  its  length  and  breadth.     Its  solid 
contents  equals  the  area  of  its  base. 

If  the  prism  is  3  units  in  height,  its  volume  is  equal  to  3 
times  the  area  of  its  base,  or  the  product  of  its  length,  breadth, 
and  thickness. 

Principles. — 1.  The  volume  of  a  rectangular  prism  is  equal 
to  the  product  of  its  length,  breadth,  and  thickness. 

2.  The  volume  of  any  prism  is  equal  to  the  product  of  the 
area  of  its  base  by  its  altitude. 

PROBLEMS 

1.  Find  the  contents  in  cubic  feet  of  prisms  having  the  fol- 
lowing dimensions: 

(a)  12  ft.  square  and  16  ft.  high. 

(b)  Base  8  ft.  by  14  ft.,  altitude  7  ft. 

(c)  Length  20  ft.,  breadth  16  ft.,  height  8  ft. 

(d)  Area  of  base  137  sq.  ft.,  altitude  9  ft. 


PRACTICAL   MEASUREMENTS  119 

#.  The  triangle  that  forms  the  base  of  the  prism  has  a  base 
of  8  ft.  and  an  altitude  of  5  ft.  The  altitude  of  the  prism 
is  10  ft.  Find  the  contents. 

8.  How  many  cubic  feet  in  a  rectangular  solid  12  ft.  by  8 
ft.  by  14  ft? 

4.  Find  the  solid  contents  of  a  hexagonal  prism  12  ft.  on  a 
side  and  16  ft.  high. 

5.  The  bottom  of  a  bin  is  a  trapezoid,  the  parallel  sides 
being  14  ft.  and  16  ft.  and  10  ft.  apart.     How  many  cubic  feet 
does  it  contain  if  it  is  8  ft.  deep? 

6.  How  many  cubic  feet  of  water  can  be  put  into  a  tank  in 
the  form  of  an  octagonal  prism,  if  it  is  9  ft.  high  and  each  side 
of  the  tank  is  8  ft.? 

7.  A  gas  reservoir  has  a  base  in  the  form  of  a  dodecagon 
16  ft.  on  a  side.     If  it  is  40  ft.  high,  how  many  cubic  feet  of 
gas  will  it  hold? 

To  Find  the  Volume  of  a  Cylinder 

214.  A  solid  having  two  equal  parallel  circles 
for  its  bases  and  a  uniformly  curved  surface  for 
its  side  is  a  Cylinder. 

Principle. — The  volume  of  a  cylinder  is  equal 
to  the  product  of  the  area  of  its  base  by  its 
altitude. 

PROBLEMS 

1.  Find  the  contents  of  cylinders  with  the  following  dimen- 
sions : 

(a)  Altitude  7  ft.,  base  6  ft.  in  diameter. 

(b)  Circumference  of  base  25  ft.,  altitude  6  ft. 

(c)  Altitude  26  ft.,  diameter  of  base  4  ft. 

(d)  Circumference  of  base  42  ft. ,  altitude  7  ft. 

2.  How  many  cubic  feet  in  a  pillar  8  ft.  in  diameter  and 
50  ft.  high? 

3.  A  cistern  7  ft.  deep  and  28  ft.  in  circumference  contains 
how  many  cubic  feet? 


120  MODERN    COMMERCIAL    ARITHMETIC 

4.  The  diameter  of  a  pipe  is  2-J-  ft.     How  much  water  will 
flow  through  it  in  an  hour,  if  it  flows  with  a  velocity  of  90  ft, 
per  minute? 

5.  How  many  cubic  feet  of  iron  in  a  pipe  80  ft.  long  and 

3  ft.  in  diameter,  if  the  iron  is  •£•"  thick? 

6.  I  wish  to  make  a  cylindrical  cistern  that  will  hold  1000 
cubic  feet  of  water.     If  I  make  it  12  ft.  in  diameter,  how  deep 
must  it  be  ? 

Brick  and  Stone  Work 

215.  Brick  work  is  commonly  estimated  by  the  1000  brick. 
Masonry  is  commonly  estimated  by  the  cubic  foot  and  by 

the  perch. 

NOTE.— A  perch  is  16J  cu.  ft.  Sometimes  24|  cu.  ft.  are  called  a 
perch. 

Usually  a  deduction  is  made  for  one-half  of  the  openings. 

216.  In  estimating  the  amount  of  work  done  in  laying 
stone  and  brick,  the  length  of  the  wall  is  found  by  measuring 
around  the  wall  on  the  outside,  or  by  measuring  on  the  inside 
and  adding  8  times  the  thickness  of  the  wall.     The  corners  are 
thus  counted  twice. 

217.  In  estimating  the  amount  of  material  used,  find  the 
exact  length  of  the  wall  by  measuring  on  the  inside  and  adding 

4  times  the  thickness  of  the  wall  for  the  corners,  or  by  measur- 
ing on  the  outside  and  subtracting  4  times  the  thickness  of  the 
wall  for  the  corners. 

Principle. — To  find  the  contents  of  a  wall,  find  the  entire 
length  of  the  wall ;  find  the  product  of  the  length,  height,  and 
thickness.  Make  deductions  for  openings. 

PROBLEMS 

1.  A  house  is  28  ft.  by  22  ft.     How  many  cubic  feet  in  the 
cellar  wall,  if  the  wall  is  18  in.  thick  and  the  cellar  is  7  ft. 
deep? 

2.  What  will  be  the  cost,  at  S0<p  a  perch   (16£  cu.  ft.),  of 
laying  a  wall  1|  ft.  thick,  for  a  cellar  29  ft.  square  and  7  ft. 
deep? 


PRACTICAL   MEASUREMENTS  121 

8.  What  will  it  cost,  at  20^  per  load  (a  cubic  yard  of  earth 
is  called  a  load),  to  have  a  cellar  dug  18  ft.  by  34  ft.,  and  8 
feet  deep?  What  will  it  cost,  at  70^  per  perch,  to  have  the 
cellar  wall  laid  20  in.  thick?  How  many  cords  of  stone  will 
be  required  for  the  wall?  (A  cord  of  stone  is  128  cu.  ft.) 

4.  Find  the  number  of  cubic  feet  in  a  cellar  wall  of  the  fol- 
lowing dimensions:    Wall,  2  ft.  thick,  8  ft.  high;    cellar,  32  ft. 
by  45  ft.     Make  ^  allowance  for  a  door  3  ft.  wide,  and  6  win- 
dows each  2  ft.  by  3  ft. 

5.  A  house  21  ft.  by  48  ft.  has  a  cellar  8  ft.  deep.     If  the 
wall  is  to  be  1^  ft.  thick,  how  many  cords  of  stone  will  be 
required  for  the  wall? 

6.  A  wall  12  in.  thick  is  estimated  to  contain  22  common 
brick  per  cubic  foot.     How  many  brick  in  a  brick  house  24  ft. 
square  and  19  ft.  high,  if  the  wall  is  1  ft.  thick  and  an  allow- 
ance is  made  for  3  doors,  each  4  ft.  by  8  ft.,  and  16  windows, 
each  34r  ft.  by  7  ft.? 

7.  Find  the  cost,  at  50^  per  load,  to  have  a  cellar  dug  20  ft. 
by  36  ft.  and  7  ft.   deep.     Find  the  cost  of  laying  the  cellar 
wall  H  ft.  thick  at  90^  per  perch.     How  many  cords  of  stone 
will  be  required? 

8.  How  many  brick  will  be  necessary  to  build  a  cistern  7  ft. 
deep,  8  ft. in  diameter,  inside  measurement,  and  1  ft.  thick? 

9.  Find  the  exact  number  of  cubic  feet  in  the  wall  of  a  cel- 
lar 34  ft.  square  (inside)    and  9  ft.  high,  if  the  wall  is  2  ft. 
thick. 

10.  Find  the  cost,  at  95^  per  perch,  of  laying  a  cellar  wall. 
The  cellar  on  the  inside  is  to  be  22  ft.  by  38  ft.  and  8  ft.  high. 
The  wall  is  to  be  2  ft.  thick,  and  the  trench  is  to  be  1^  ft.  deep. 

Wood 

218.  A  Cord  of  wood  is  equivalent  to  128  cu.  ft. — or  a  pile 
8  ft.  by  4  ft.  by  4  ft.  A  Cord  Foot  (cd.  ft.)  is  1  ft.  in  length 
of  such  a  pile,  or  16  cu.  ft. 

NOTE.— A  pile  of  wood  8  ft.  long  and  4  ft.  high  is  commonly  called 
a  cord  without  regard  to  the  length  of  the  wood.  Thus,  a  cord  of 
stove  wood  is  a  pile  8  ft.  by  4  ft.  by  the  length  of  the  sticks  of  wood. 


122  MODERN    COMMERCIAL   ARITHMETIC 

219.  The  face  of  a  cord  of  wood  measures  32  sq.  ft.  (8x4). 
Therefore,  the  area  of  the  face  of  such  a  pile  divided  by  32 
equals  the  number  of  cords  in  the  pile. 

PROBLEMS 

1.  Find  the  number  of  cords  of  wood  in  piles  having  the 
following  dimensions: 

(a)  Stove  wood,  38  ft.  by  9  ft.  (d)  4-ft.  wood,  27  ft.  by  5  ft. 
(J)  Stove  wood,  28  ft.  by  6  ft.  (e)  4-ft.  wood,  38  ft.  by  6  ft. 
(e)  4-ft.  wood,  16  ft.  by  3  ft. 

2.  A  man  bought  a  pile  of  wood  16  ft.  long,  9  ft.  wide,  and 
7  ft.  high.     What  did  it  cost  at  $3  per  cord  of  128  cu.  ft.? 

3.  A  pile  of  wood  is  begun  4  ft.  wide  and  6  ft.  high.     How 
long  must  it  be  made  to  contain  18  cords? 

4.  A  wood  rack  is  12  ft.  long  and  3  ft.  wide.     How  high 
must  the  wood  be  piled  upon  it  to  make  1£  cords? 

Lumber 

220.  If  a  board  is  not  more  than  1  in.  thick,  a  square  foot 

of  its  surface  is  a  foot  of  lumber,  or  a 
foot  board  measure. 

A  board  1  ft.  wide  and  14  ft.  long, 
if  not  more  than  1  in.  thick,  contains 
14  ft.  of  lumber. 

The  width  of  boards  is  measured  in 
inches. 

221.  For  boards  not  more  than  1  in.  thick,  we  have  the 
formula : 

Length  (ft.)  x  width  (in.)  £  .      , 

— ^ — '-  =  feet  of  lumber 

12 

222.  If  lumber  is  more  than  1  in.  thick,  this  formula  is 
used: 

Length  (ft.)  x  width  (in.)  x  thickness  (in.)  =  f ^  rf  lumber 
12 


PRACTICAL   MEASUREMENTS  123 

EXAMPLE. — Find  the  number  of  feet  of  lumber  in  a  board, 
not  more  than  1  in.  thick,  with  length  12  ft.,  width  13  in. 

OPERATION  NOTE.— Use   cancellation    when    practicable. 

12  x  13-5-12  =  13      ^se  an(luot  parts  of  12.     If  a  board  is  8  in.  wide 

and  15  ft.  long,  say  8  X  1J  =  10,  instead  of  8 

X  U>  -f-  12  =  10.  Likewise,  as  parts  of  12,  3  =  J,  4  =  J,  6=  J,  8  =  |, 
9  =  5,  15  =  li,  16  =  1J,  18  =  1J. 

PROBLEMS 

Find  the  number  of  feet  of  lumber  in  boards,  not  more  than 
1  in.  thick,  of  the  following  dimensions: 

1.  Length  15  ft.,  width  16  in.       5.  Length  24  ft.,  width  16  in. 

2.  Length  14  ft.,  width    9  in.       6.  Length  22  ft.,  width    6  in. 
S.  Length  18  ft.,  width  10  in.       7.  Length    8  ft.,  width    9  in. 
4.  Length  20  ft.,  width  15  in.       8.  Length  14  ft.,  width  13  in. 

Find  the  number  of  board  feet  in  timbers  and  plank  of  the 
following  dimensions: 

9.  Width  8  in.,  length  16  ft.,  thickness  2|  in. 

10.  Width  12  in.,  length  14  ft.,  thickness  3  in. 

11.  Width  14  in.,  thickness  4  in.,  length  10  ft. 

12.  Length  18  ft.,  width  12  in.,  thickness  9  in. 

13.  Length  20  ft.,  8  in.  square. 

14.  Length  16  ft.,  2  in.  by  6  in: 

15.  Length  18  ft.,  2  in.  by  4  in. 

16.  Length  14  ft.,  2  in.  by  8  in. 

17.  Length  15  ft.,  2  in.  by  4  in. 

18.  Find  the  cost,  at  $18.50  per  M,  of  32  scantling,  each 
14  ft.  by  2  in.  by  4  in. 

19.  Find  the  cost,  at  $36  per  M,  of  12  timbers,  each  18  ft. 
long  and  10  in.  square. 

20.  Find  the  cost,  at  $14  per  M,  of  a  load  of  hemlock  tim- 
bers of  the  following  dimensions : 

24  scantling 16' x  2"  x  4" 

12  scantling 14'  x  2"  x  6" 

8  timbers 12'  x  6"  x  8" 

10  timbers 16'  x  4"  x  4" 

20  plank 18'  x  2"  x  10" 

6  timbers  .  14'  x  4"  x    6" 


124  MODERN    COMMERCIAL   ARITHMETIC 

21.  Find  the  cost,  at  $28  per  M,  of  the  following  pieces  of 
pine: 

22  plank 16'  x  2  "  x  12" 

18  plank 14'  x  3  "  x  10" 

25  scantling 18'  x  2  "  x    4" 

6  sticks 14'  x  4  "  x    4" 

40  boards 12'  x  1|"  x    8" 

36  rafters 18'  x  2  "  x    6" 

48  sleepers 16'  x  2  "  x    8" 

8  sticks 24'  x  6  "x    8" 

22.  Find  the  cost  of  the  following  chestnut  lumber  at  $45 
per  M: 

9  pieces 12' x  1£"  x  10" 

12  pieces 14' x  1  "x  12" 

10  pieces 16'  x  1£"  x  14" 

6  pieces 12'  x  1  "  x  14" 

8  pieces 8' x  2  "x    6" 

9  pieces 6' x  !£"  x    8" 

23.  What  is  the  cost  of  the  following  boards  at  $18  per  M: 

16  boards 12'  x    f"  x  12" 

12  boards 16'  x    $"  x  10" 

20  boards 18'  x    f "  x  12" 

10  boards 14'  x  1  "  x    9" 

24  boards 12'  x    i"  x    8" 

15  boards 9'  x  1£"  x  10" 

Capacity  of  Bins  and  Cisterns 

223.  TABLE' 

2150.4  cu.  in.  =  1  bu. 

231     cu.  in.  =  1  gal. 

311      gal.     =  1  bbl. 

FORMULAS 

Length  x  breadth  x  thickness  x  1728 

• =  bushels 

2150.4 

Length  x  breadth  x  thickness  x  1728 

2 =  gallons 

231 
NOTE. — All  dimensions  should  be  in  feet. 


PRACTICAL   MEASUREMENTS  125 

PROBLEMS 

1.  Find  the  contents  (dry  measure)  of  the  following:     (a)  A 
bin  8  ft.  square  and  6  ft.  deep ;  (b)  a  box  9  ft.  by  3  ft.  4  in. 
by  10  in. ;  (c)  a  box  6  ft.  long,  4  ft.  high,  4^-  ft.  wide. 

2.  How  many  bushels  of  wheat  will  a  bin  hold  that  is  8  ft. 
long,  5  ft.  wide,  and  5£  ft.  high? 

8.  How  many  bushels  of  potatoes  will  a  bin  hold  that  is  9  ft. 
square  and  6^  ft.  deep? 

4.  How  many  bushels  of  apples  will  a  wagon  box  hold  that 
is  14  ft.  by  3  ft.  4  in.  by  2  ft.  3  in.? 

5.  Find  the  contents,  liquid  measure,  of  a  tank  9  ft.  long, 
4  ft.  wide,  and  3  ft.  deep. 

6.  How  many  barrels  will  a  cistern  hold  that  is  7  ft.  by  8 
ft.  by  6  ft.? 

7.  A  vat  8^  ft.  by  6  ft.  by  4  ft.  will  hold  how  many  gallons 
of  water? 

8.  A  cylindrical  cistern  7  ft.  in  diameter  and  7  ft.  high  will 
hold  how  many  barrels  of  vinegar? 

9.  If  3  measures  of  grapes  will  make  2  measures  of  wine, 
how  many  gallons  of  wine  can  be  made  from  3  bu.  of  grapes? 

10.  How  many  gallons  of  alcohol  will  be  required  to  fill  a 
pipe  18  ft.  long  and  1-J-  in.  in  diameter? 

11.  How  many  gallons  of  oil  in  a  cylindrical  can  2  ft.  high 
and  14  in.  in  diameter? 

12.  If  1  cu.  ft.  of  water  weighs  62£  lb.,  how  many  gallons 
in  1  T.  of  water? 

13.  A  tank  is  22  ft.  in  circumference  and  8  ft.  high.     How 
many  barrels  of  beer  (28  gal.)  will  it  contain? 

PRACTICAL  RULES  FOR  DEALERS  IN  FARM  PRODUCE 

224:.  The  following  rules  are  approximate: 

1.  To  find  the  contents,  in  bushels,  of  a  bin  or  box,  multiply 
the  number  of  cubic  feet  by  .8. 

2.  To  find  the  volume  of  a  bin  required  to  hold  a  given 
number  of  bushels,    divide  the  number  of  bushels  by  .8,  or 
multiply  by  f . 


126  MODERN    COMMERCIAL   ARITHMETIC 

3.  To  find  the  contents,  in  40-qt.  bushels,  of  a  bin,  multiply 
the  number  of  cubic  feet  by  £ . 

NOTE. — The  40-qt.  or  "heaped"  bushel  is  used  for  apples,  potatoes, 
etc. 

4>  To  find  the  volume  of  a  bin  required  to  hold  a  given 
number  of  40-qt.  bushels,  divide  the  number  of  bushels  by  £ . 

5.  To  find  the  contents,  in  gallons,  of  a  tank  or  cistern, 
multiply  the  number  of  cubic  feet  by  7-|. 

6.  To  find  the  volume,  in  cubic  feet,  of  a  tank  required  to 
hold  a  given  number  of  gallons,  divide  the  number  of  gallons 
by  7V 

7.  To   find   the   number   of   shelled   bushels  in  a  crib  of 
unshelled  corn,  multiply  the  number  of  cubic  feet  by  .45. 

NOTE. — Pupils  should  be  required  to  give  the  reasons  for  the  above 
rules.  NOTE— A  bushel  is  to  a  cubic  foot  as  56  is  to  45. 

Hay 

225.  The  weight  of  hay,  per  cubic  foot,  in  a  load,  shed, 
mow  or  stack,  varies  with  the  kind  of  hay,  the  height  of  the 
pile,  pressure  or  treading  in  packing,  and  time  of  settling. 
The  higher  the  pile  the  more  compact  the  hay  will  be. 

Principles. — 1.  To  find  the  weight  of  hay  in  a  load,  or  low 
pile,  allow  540  cu.  ft.  for  a  ton. 

2.  To  find  the  weight  of  hay  in  an  ordinary  mow,  or  low 
stack,  allow  400  cu.  ft.  for  a  ton. 

3.  To  find  the  weight  of  hay  in  mow  bottoms  and  in  bot- 
toms of  high  stacks,  allow  325  cu.  ft.  per  ton. 

PROBLEMS 

1.  How  many  bushels  of  wheat  in  a  bin  6  ft.  square  and  4 
ft.  deep? 

2.  How  many  bushels  of  apples  in  a  wagon  box  14  ft.  long, 
3  ft.  wide,  and  30  in.  high. 

3.  How  many  bushels  of  oats  in  a  bin  8  ft.  long,  6  ft.  wide, 
and  3  ft.  deep? 

4.  At  35^  per  bushel,  find  the  value  of  a  bin  of  potatoes 
10  ft.  long,  7  ft.  wide,  and  5  ft.  high. 


PRACTICAL   MEASUREMENTS  127 

5.  How  many  cubic  feet  of  space  must  be  provided  for  500 
bushels  of  apples?     If  the  bin  is  4  ft.  deep  and  8  ft.  wide,  how 
long  must  it  be? 

6.  I  wish  to  build  a  bin  that  will  hold  120  bushels  of  wheat. 
If  I  make  it  6  ft.  square,  how  high  must  it  be? 

7.  How  many  cubic  feet  in  a  cylindrical  cistern  5  ft.  in 
diameter  and  6  ft.  deep?     How  many  gallons  would  it  hold? 

8.  How  deep  must  a  cistern  be  to  hold  60  bbl.  of  water  if  it 
is  7  ft.  in  diameter? 

9.  How  many  bushels  of  shelled  corn  in  a  crib  of  unshelled 
corn  18ft.  by  6ft.  by  7ft.? 

10.  If  a  bin    will  hold  400  bushels  of  wheat,  how  many 
bushels  of  apples  will  it  hold? 

11.  A  wagon  box  14  ft.  long,  3  ft.  wide  and  2-J-  ft.  high  is 
full  of  corn  in  the  ear.     How  many  bushels  of  shelled  corn  will 
the  load  make? 

12.  How  many  bushels  of  turnips  in  a  bin  7  ft.  long,  5  ft. 
wide,  and  4  ft.  deep? 

13.  I  wish  to  make  a  wagon  box  to  hold  40  bu.  of  apples. 
If  I  make  it  14  ft.  long  and  3  ft.  wide,  how  high  must  it  be? 

14-  How  many  hundredweight  of  hay  in  a  load  20  ft.  long, 
12  ft.  wide,  and  7  ft.  high? 

15.  The  top  of  a  high  hay  stack  has  been  removed.     The 
bottom  is  20  ft.  square  and  12  ft.  high.     How  many  tons  does 
it  contain? 

16.  A  pile  of  hay  40  ft.  long,  15  ft.  wide,  and  9  ft.  high 
contains  how  many  tons? 

17.  If  a  stack  of  hay  is  24  ft.  in  diameter,  and  12  ft.  high, 
what  is  it  worth  at  $12  per  ton? 

18.  I  wish  to  build  in  a  barn  a  bay  that  will  hold  100  tons 
of  packed  hay.     If  I  make  it  40  ft.  wide  and  12  ft.  deep,  how 
long  must  it  be? 

19.  How  many  cubic  feet  of  space  will  be  required  to  hold 
400  bu.  of  potatoes?     If  the  bin  is  made  12  ft.  square,  how 
deep  must  it  be? 

20.  A  bin  that  will  hold  250  bu.  of  wheat  will  hold  how 
many  bushels  of  potatoes? 


128  MODERN    COMMERCIAL    ARITHMETIC 

SQUARE   ROOT   AND   ITS  APPLICATIONS 

226.  To  square  a  number  is  to  multiply  it  by  itself.     The 
square  of  5  is  25.     36  is  the  square  of  6.     What  is  the  square 
of  8,  9,  11,  12,  15,  20,  25? 

227.  One  of  the  two  equal  factors  of  a  number  is  the  square 
root  of  the  number.     Thus,  10  and  10  are  the  two  equal  factors 
of  100,  and  10  is  the  square  root  of  100.     12  is  the  square  root 
of  144.     What  is  the  square  root  of  81,  121,  225,  625? 

228.  To  indicate  the  square  of  a  number  we  write  a  small 
figure  2  at  the  upper  right  hand  side  of  the  number.     Thus, 
122  means  12  x  12,  or  12  squared.     152  =  225.     Give  the  value 
of  82;  108;  II2;  132;  212;  192. 

229.  To  indicate  the  square  root  of  a  number,  we  write 
the  character  ^/  at  the  left  of  the  number.     \/100  means  the 
square  root    of  100,  or  10.     \/144  =  12.      Give  the  value  of 
\/225;  v/625;  \/900;  v/169;  \/400. 

230.  Principles. — 1.  If  the  side  of  a  square  represents  a 
number,  the   square   itself  will   represent  the  square  of   the 
number. 

2.  If  a  square  represents  a  number,  a  side  of  the  square 
will  represent  the  square  root  of  the  number. 


MENTAL  PROBLEMS 

1.  I  wish  to  make  a  square  table  with  a  surface  of  16  sq. 
ft. ;  what  musfc  be  the  length  of  a  side? 

2.  What  is  the  length  of  a  side  of  a  square  board  that  con- 
tains 225  sq.  in.? 

3.  What  is  the  length  in  rods  of  a  square  field  that  contains 
10  acres? 

4-  A  square  floor  contains  400  sq.  ft.  of  space ;  what  is  the 
length  of  one  side? 


PRACTICAL   MEASUREMENTS 


129 


The  diagram  compares  a 
square  with  the  square  of  a 
number  and  the  side  of  the 
square  with  the  square  root  of 
the  same  number.  The  large 
square  marked  T2  equals  the 
square  of  the  tens  of  the  num- 
ber. The  area  of  the  square  is 
100  and  the  square  of  10  is  100. 
Each  of  the  rectangles  marked 
T  X  U  equals  the  product  of 
the  tens  by  the  units.  The 
small  square  marked  U2  equals 
the  square  of  the  units. 

The  complete  square  equals 
the  square  of  the  tens  plus 

twice  the  product  of  the  tens  and  units,  plus  the  square  of  the  units, 
or  T2  +  2TU  +  U2.  13  =  10  +  3,  or  IT  -+  3U.  132  =  102  +  2  (10  X  3) 
+  32,  or  T2  +  2TU  +  U2.  Any  number  may  be  considered  as  composed 
of  tens  and  units.  125  is  composed  of  12  tens  and  5  units.  1252  =  T2 
+  2TU  +  U2,  or  1202  +  2  (120  X  5)  +  52.  2654  =  265  tens  +  4  units. 
26542  ==  26502  +  2  (2650  X  4)  +-  42. 

The  following  example  also  shows  the  relation  of  a  number 
to  its  square. 

EXAMPLE. — Find  the  square  of  10  plus  3. 


T  X  U  =  30 

U2  =  9 

CO 

T2  =  100 

TXU 

o 

10 

3 

OPERATION 


10  +  3 
10  +  3 


102 


(10  x  3)  +  3* 
(10  x  3) 


102  +  2  (10  x  3)  +  32  =  169  =  T2  +  2TU  +  IP 

Principle. — The  square  of  a  number  composed  of  tens  and 
units  is  equal  to  the  square  of  the  tens  +  2  x  the  tens  x  the 
units  +  the  square  of  the  units. 


PROBLEMS 

Write  out  the  squares  of  the  following : 

1.  5T  +  4U.  8.  60  +  8. 

2.  40  +  3.  4-  ^0  +  5. 


5.  80  +  4. 


130  MODERN    COMMERCIAL   ARITHMETIC 

Write  by  inspection  the  square  root  of : 

6.  100  +  60    +    9.        8.  100+    80  +  16.        10.  100  +  140  +  49. 

7.  100  +  100  +  25.        9.   100  +  120  +  36.         11.  400  +  200  +  25. 

To  Find  the  Square  Root  of  a  Number 

231.  Finding  the  square  root  of  a  number  is  an  operation 
in  " fitting  and  trying"  like  long  division.  We  try  and  then 
find  whether  we  are  right.  We  can  tell  something  about  the 
square  root  of  a  number  by  inspection.  Study  the  following 
table :  . 

12=    1  102=    100  1002=    10000 

92  =  81  992  =  9801  9992  =  998001 

It  will  be  seen  that  the  square  of  a  number  of  1  figure  cannot  con- 
tain more  than  two  figures ;  that  the  square  of  a  number  of  2  figures 
cannot  contain  less  than  three  nor  more  than  4  figures ;  that  the  square 
of  a  number  of  3  figures  cannot  contain  less  than  5,  nor  more  than  6 
figures.  If  any  number  be  separated  into  periods  of  2  figures  each, 
beginning  at  the  right,  there  will  be  just  as  many  periods  as  there 
are  figures  in  the  square  root  of  the  number.  Thus,  in  the  square 
root  of  1 '  46 '  75 '  83  there  are  4  figures ;  in  the  square  root  of  21 '  38 '  00 
there  are  three  figures. 

The  first  figure  of  the  square  root  of  a  number  will  always  be  the 
highest  figure  whose  square  can  be  formed  in  the  first  (left  hand) 
period.  If  the  first  period  is  1,  the  first  figure  of  the  root  will  be  1.  If 
the  first  period  is  6,  the  first  figure  of  the  root  will  be  2.  If  the  first 
period  is  28,  the  first  figure  of  the  root  will  be  5.  What  will  be  the 
first  figure  of  the  root  if  the  first  period  is  36;  40;  49;  55;  60;  65;  75; 
85;  98? 

Find  the  number  of  figures  in  the  root,  and  the  first  figure  which  is 
always  sure  to  be  right,  then  proceed  to  find  the  next  figure.  This  is 
found  somewhat  as  a  quotient  figure  in  division  is  found.  After  two 
figures  of  the  root  are  found,  call  them  both  tens — consider  them  as 
one — and  find  the  next  figure,  and  so  on. 

EXAMPLE  1. — Find  the  square  root  of  169. 
OPERATION  EXPLANATION. — There  are  two  periods  and 

1'69  I  13  there  will  be  two  figures  in  the  root.  The 
first  figure  of  the  root  must  be  1.  Take  the 
square  of  1  (1  ten)  from  the  whole  square  (169) 


20 
23 


69 
69 


and  69  is  left.     69  is  2  X  the  tens  -f-  the  square 
of  vthe   units,    or   2TU  X  U,  or    U(2T  +  U). 
Now  find  the  next  figure,  or  U,  the  number 
wfeich  multiplied  by  twice  the  tens  plus  itself  will  produce  69.     At  the 


PRACTICAL   MEASUREMENTS  131 

left  of  69  write  2  X  the  tens,  or  20,  and  by  inspection  the  next  figure 
is  found  to  be  3.  Add  3  to  twice  the  tens  already  found  and  get  23, 
(2T  +  U).  Multiply  this  by  3  and  it  is  found  that  the  estimate  was 
correct. 

EXAMPLE  2. — Find  the  square  root  of  6770404. 

OPERATION  EXPLANATION.— There  will  be    four 

6'77'04'04  I  2602      figures  in  the  root.     The  first  figure  of 
.  the  root  is  2,  for  the  greatest  square  in 

the  first  period  is  4.     Taking  the  square 


40 

46 


277 
276 


of  2  from   the   first   period,    2  is  left. 

Bringf  down  the  next  period  and  from 
5200  10404  the  result,  277,  find  the  next  figure  of 

5202  10404  the  root.     277  is  twice  the  first  figure  X 

the  second  +  the  square  of  the  second 

+  a  possible  remainder.  To  find  the  second  figure  divide  277  by  twice 
2  tens,  the  first  root  figure,  or  40,  and  get  6,  which  is  probably  the 
second  figure  of  the  root.  Add  6  to  40,  and  then  multiply  46  by  6 
instead  of  multiplying  40  by  6  and  adding  6x6.  Subtract  276,  (46  X  6), 
from  277  and  obtain  1.  Bring  down  the  next  period  and  the  result 
is  104.  Divide  this  by  twice  the  first  figure  of  the  root,  which  is  now 
26  tens,  to  find  the  second  figure.  Twice  26  tens  are  520  (26  X  2  with 
one  cipher  annexed).  But  520  is  not  contained  in  104,  so  the  next 
figure  of  the  root  is  0.  Call  260  tens  the  first  figure  of  the  root,  and 
proceed  to  find  the  last  figure.  Bring  down  the  next  period  and 
10404  is  the  dividend.  Divide  it  by  twice  the  found  part  of  the  root 
(260  tens),  which  is  5200  (260  X  2  with  one  cipher  annexed).  The  quo- 
tient is  2.  Add  2  to  the  "trial  divisor,"  5200,  and  the  "complete 
divisor"  is  5202. 

Then  divide  10404  by  5202,  and  the  quotient  is  exactly  2. 

Steps. — 1.  Beginning  at  the  left  point  off  into  periods  of  2 
figures  each. 

2.  Find  the  first  figure  of  the  root. 

3.  Take  the  square  of  the  first  figure  from  the  first  period 
and  bring  down  the  next  period. 

4-  At  the  left  write  twice  the  part  of  the  root  already  found 
and  annex  one  cipher. 

5.  Estimate  the  next  figure  of  the  root. 

6.  Add  this  new  figure  to  the  trial  divisor  of  the  fourth 
step. 


132  MODERN    COMMERCIAL    ARITHMETIC 

• 

7.  Divide  and  bring  down  the  next  period. 

8.  Kepeat  4,  5,  6,  7,  and  so  on. 

NOTES.— 1.  If  at  any  time  the  product  of  the  divisor  and  last  fig- 
ure of  the  root  is  greater  than  the  dividend,  the  quotient  figure  is  too 
great  and  must  be  made  less — the  same  as  in  long  division. 

2.  If  there  is  a  remainder  after  finding  the  last  integral  figure  of 
the  root  ciphers  may  be  annexed,  and  the  root  continued  as  a  decimal. 

PROBLEMS 
Find  the  square  root  of : 

1.  576.  4.  1522756.  7.  15876. 

2.  5625.  5.  7  to  3  decimal  places.         8.  2645731. 

3.  42436.  6.  2.  9.  ff. 

NOTE — In  extracting  the  square  root  of  a  fraction  the  root  of  each 
term  may  be  found  separately,  or  the  fraction  may  first  be  reduced  to 
a  decimal. 

10.  Extract  the  square  root  of  -Jf. 

11.  What  is  the  length  of  the  side  of  a  square  lot  that  con- 
tains 15  A.? 

12.  A  man  wishes  to  set  out  15625  trees  in  a  square  so  that 
there  shall  be  the  same  number  of  trees  in  rows  each  way. 
How  many  trees  should  be  planted  in  a  row? 

IS.  How  many  hills  of  potatoes,  each  3  ft.  from  the  others 
in  rows  3  ft.  apart,  can  be  planted  in  an  8-A.  square  lot? 

14.  At  $1.40  per  rod,  what  will  it  cost  to  fence  a  field  of 
28  A.  twice  as  long  as  it  is  wide? 

15.  A  man  wishes  to  erect  a  building  having  2900  feet  of 
floor.     If  he  wishes  its  length  to  be  four  times  its  width,  what 
must  be  its  dimensions? 

To  Find  the  Area  of  a  Triangle  by  Square  Root 

232.  EXAMPLE. — Find  the  area  of  a  triangle  whose  sides 
are  12  ft.,  8  ft.,  and  16  ft.,  respectively. 

Steps  in  the  Operation. — 1.  Add  the  three  sides  and  divide 
the  sum  by  2. 

2.  From  this  half-sum  subtract  each  side  separately. 


PRACTICAL   MEASUREMENTS  133 

3.  Find  the  product  of  the  three  remainders  and  the  half- 
sum. 

4.  Extract  the  square  root  of  the  product.     This  will  give 
the  area. 

OPERATION 

8  +  12  +  16  =  36 
36+  2  =  18 
18-  8  =  10 
18-12=  6 
18-16=  2 
18  x  10  x  6  x  2  =  2160 


N/2160  =  46.475,  area  in  square  feet 

PROBLEMS 

1.  The  sides  of  a  triangle  measure  21  ft.,  40  ft.,  and  45  ft. 
Find  the  area  of  the  triangle. 

2.  How  many  acres  in  a  triangular  field  whose  sides  measure 
48  rd.,  62  rd.,  and  78  rd.? 

3.  How  many  square  feet  in  the  gable  end  of  a  building 
that  is  80  ft.  wide,  if  the  length  01  each  side  of  the  roof  is 
50  ft.? 

4.  How  many  acres  in  a  triangular  field  which  measures 
36  rd.,  24  rd.,  and  42  rd.? 

5.  What  is  the  diameter  of  a  circular  field  that  contains 
1  acre? 

NOTE. — Diameter2  X  .7854  =  area. 

6.  Each  side  of  a  triangle  is  62  ft.     What  is  its  area? 

7.  If   the   area  of  a  circular  field  is  10  A.,  what   is  its 
diameter? 

8.  How  many  rods  of  netting  must  be  purchased  to  enclose 
a  circular  park  of  %  acre? 

9.  What  is  the  diameter  of  a  pipe  if  the  area  of  a  cross- 
section  is  8  sq.  ft.? 

10.  What  is  the  area  of  a  triangle  whose  sides  are  23  rd. , 
28  rd.,  and  31  rd.? 

11.  A  fence  100  yd.  long  will  enclose  how  much  land  in  the 
form  of  a  circle?     How  much  in  the  form  of  a  square? 


134  MODERN    COMMERCIAL    ARITHMETIC 

12.  Find  the  diameter  of  a  circle  equal  in  area  to  a  square 
12  ft.  on  a  side. 

IS.  Find  the  side  of  a  square  equal  in  area  to  a  circle  whose 
diameter  is  100  ft. 

14.  If  a  cistern  is  to  be  6  ft.  deep,  what  must  be  its  diam- 
eter in  order  that  it  may  contain  50  bbl.? 

15.  The  three  sides  of  a  field  are  75  rd.,  60  rd.,  and  53  rd. 
What  is  its  area? 

16.  I  wish  to  build  a  bin  that  will  hold  1000  bushels  of 
wheat.     If  I  make  it  4  ft.  deep,  how  large  square  must  it  be? 

17.  Find  the  area  of  a  triangle  whose  sides  are  19  yd., 
21  yd.,  and  24yd. 

18.  Find  the  contents  in  bushels  of  a  bin  5  ft.  deep,  whose 
bottom  is  an  equilateral  triangle  8  ft.  on  a  side. 

19.  Find  the  number  of  square  feet  of  roofing  on  a  house 
40  ft.  square.     The  roof  consists  of  4  parts,  each  slanting  from 
a  side  of  the  house  to  the  peak  in  the  center.     The  distance 
from  the  peak  to  one  corner  of  the  roof  is  80  ft. 

20.  What  is  the  area  of  a  triangle  whose  sides   measure 
20ft.,  24ft.,  and  30  ft.? 

The  Eight  Triangle 

233.  The  Eight  Triangle,  or  a  Eight-Angle  Triangle,  is  a 
triangle  having  one  right  angle. 

234.  The  side  opposite  the  right  angle  is  the  Hypotenuse. 

If  the  base  is  4  and  the  altitude  3, 
the  hypotenuse  is  5. 

NOTE. — As  shown  in  the  diagram,  if  a 
square  is  drawn  on  each  side  of  a  right 
triangle  the  square  on  the  side  of  the 
hypotenuse  is  equal  to  the  sum  of  the 
squares  on  the  other  two  sides. 

This  is  true  of  any  right  triangle. 

Principle. — In  any  right  triangle, 
the  square  of  the  hypotenuse  is  equal 
to  the  sum  of  the  squares  of  the  other  two  sides. 


PRACTICAL   MEASUREMENTS  135 

Hypotenuse2  =  base2  -f  altitude2 
B2  =  H2  -  A2 
A2  =  H2-B2 

EXAMPLE  1. — The  hypotenuse  of  a  right  angle  is  10  and 
the  altitude  is  6.     What  is  the  base? 

OPERATION 

B2  =  102  -  62 

B2  =  100- 36,  or  64 

B  =  \/64,  or  8 

EXAMPLE  2. — The  base  of  a  triangle  is  12  ft.,  the  altitude 
is  16  ft.     Find  the  hypotenuse. 

OPERATION 

H2  =  162  +  122 

H2  =  2564- 144,  or  400 

H  =  v/400,  or  20 


PROBLEMS 

1.  The  hypotenuse  is  15  yd.,  the  base  is  12  yd.     What  is 
the  altitude? 

2.  If  the  altitude  is  15  ft.,  the  base  20  ft.,  what  is  the 
hypotenuse? 

3.  How  many  acres  in  a  field  in  the  form  of  a  right  triangle 
if  the  hypotenuse  is  70  rd.  and  the  base  is  56  rd.? 

4.  Find  the  diagonal  of  a  square  22  ft.  on  a  side. 

5.  Find  the  distance  from  the  lower  southeast  corner  of  a 
room  to  the  upper  northwest  corner,  if  the  room  is  18  ft.  by 
16  ft.,  and  10ft.  high. 

6.  I  wish  to  put  a  steel  brace  against  a  brick  wall.     If  the 
brace  is  to  meet  the  wall  18  ft.  above  the  base,  and  is  to  stand 
7  ft.  from  the  foot  of  the  wall,  how  long  must  the  brace  be? 

7.  How  long  must  a  wire  be  to  reach  from  the  top  of  a 
stack  60  ft.  high  to  a  stake  45  ft.  from  the  base  of  the  stack? 

8.  Find  the  area  of  the  surface  of  the  sides  of  a  squaro 
pyramid  125  ft.  on  a  side,  if  the  apex  is  90  ft.  above  the  base. 


136  MODERN    COMMERCIAL    ARITHMETIC 

9.  There  are  two  poles  90  ft.  apart,  each  110  ft.  high. 
How  far  is  it  from  the  top  of  one  to  the  middle  of  the  other? 

10.  What  must  be  the  length  of  the  rafter  of  a  house  28  ft. 
wide,  if  the  peak  of  the  roof  is  to  be  10  ft.  above  the  plate  and 
the  roof  is  to  project  1|-  ft.? 

11.  What  is  the  size  of  the  largest  square  that  can  be  cut 
out  of  a  circular  sheet  of  metal  2  ft.  in  diameter  ? 

12.  Find  the  area  of  a  right  triangle  whose  base  is  64  ft. 
and  hypotenuse  80  ft. 

13.  What  is  the  distance  from   a   point  to   the   top   of   a 
pole  120  ft.  high,  if  the  pole  is  90  ft.  from  the  place  of  meas- 
urement? 

14*  What  is  the  length  of  the  diagonal  of  a  room  18  ft.  by 
28  ft? 

15.  Find  the  area  of  the  six  faces  of  a  hexagonal  pyramid 
8  ft.  on  a  side,  the  distance  from  the  apex  to  any  corner  at  the 
base  being  20  ft. 

REVIEW  PROBLEMS  IN  MENSURATION 

1.  Find  the  area  of  a  circle  15  ft.  in  diameter. 

2.  How  many  square  feet  in  the  floor  of  a  hexagonal  room 
10  ft.  on  a  side? 

3.  How  many  feet  of  lumber  in  a  board  18  ft.  by  11  in.  and 
1|  in.  thick? 

4-  What  is  the  contents  in  bushels  of  a  bin  9  ft.  square  and 
6  ft.  deep? 

5.  How  many  cords  of  wood  in  a  pile  38  ft.  long,  7  ft.  high 
and  4  ft.  wide? 

6.  How  much  liquid  will  be  required  to  fill  a  pipe  f  in.  in 
diameter  and  25  ft.  long? 

7.  How  many  square  feet  of  sheet  iron  will  be  required  to 
build  a  smokestack  45  ft.  high  and  14  in.  in  diameter? 

8.  What  is  the  value,  at  $68  per  acre,  of  a  triangular  field 
which  measures  36  rd.,  42  rd.,  and  54  rd.? 

9.  What  will  it  cost,  at  20^  per  square  foot,  to  pave  the 
intersecting  diagonal  walks  of  a  park  40  yd.   square,  if  the 
walks  are  6  ft.  wide.? 


PRACTICAL   MEASUREMENTS  137 

10.  How  many  cubic  feet  of  marble  in  a  cylindrical  monu- 
ment 9  ft.  in  diameter  and  32  ft.  high? 

11.  How  many  bricks  in  a  chimney  6  ft.  square  and  48  ft. 
high,  if  the  chimney  wall  is  1  ft.  thick? 

12.  Find  the  number  of  yards  of  carpet,  f  yd.  wide,  neces- 
sary to  cover  the  floor  of  a  room  21  ft.  by  25  ft. 

13.  If  water  weighs  62£  Ib.  per  cubic  foot,  what  is  the 
weight  of  the  water  in  a  tank  which  measures  4  ft.  by  2£  ft.  by 
14ft.? 

14.  How  many  feet  of  lumber  in  a  timber  8"  x  9"  and  28  ft. 
long? 

15.  How  many  feet  of  fence  will  enclose  a  square  field  of 
8  A.? 

16.  Find  the  number  of  cubic  feet  of  masonry  in  the  walls 
of  a  cellar  16  ft.  square  on  the  inside  and  9  ft.  deep,  if  the  wall 
is  20  in.  thick. 

17.  How  many  loads  of  earth  must  be  removed  in  digging  a 
cellar  20  ft.  wide,  46  ft.  long,  and  7  ft.  deep? 

18.  Find  the  capacity  in  barrels  of  a  tank  4  ft.  wide,  10  ft. 
long,  and  5  ft.  deep. 

19.  What  will  be  the  cost,  at  $28  per  M,  of  a  stick  of  timber 
26  ft.  long,  12  in.  wide,  and  9  in.  thick? 

20.  How  many  square  yards  of  plastering  are  there  on  the 
walls  and  ceiling  of  a  room  21  ft.  wide,  27  ft.  long,  and  11  ft. 
high,  allowing  for  7  doors  4  ft.  wide  and  8  ft.  high,  and  for 
8  windows  4  ft.  wide  and  7  ft.  high? 

21.  How  many  cords  of  stone  will  be  used  in  building  a 
foundation  wall  for  a  factory  80  ft.  by  110  ft.,  if  the  wall  is  to 
be  10  ft.  high  and  2£  ft.  thick? 

22.  How  many  brick  will  be  used  in  erecting  a  brick  house 
24  ft.  wide,   36  ft.  long,  and  18  ft.  high,  if  the  wall  of  the 
house  is  made  1^  ft.  thick,  and, allowing  for  3  doors  3^  ft.  by 
?i  ft.,  and  for  24  windows  each  3£  ft.  by  6  ft.? 

NOTE. — 22  brick  will  make  a  cubic  foot  of  wall. 

28.  How  many  feet  of  lumber  in  a  stick  14  ft.  long,  9  in. 
wide  and  6  in.  thick? 


138  MODERN   COMMERCIAL   ARITHMETIC 

24.  How  much  lumber  will  be  required  to  build  a  fence 
6  boards  high  around  a  square  lot  of  4  acres,  if  the  boards  are 
6  in.  wide  and  are  to  be  nailed  to  posts  4  in.  square  and  8  ft. 
long,  set  8  ft.  apart?  How  many  posts? 

25.  A  bin  6  ft.  by  9  ft.  by  5  ft.  will  contain  how  many 
bushels  of  potatoes? 

26.  A  builder  has  planned  a  house  27  ft.  by  45  ft.     How 
many  feet  of  lumber  will  be  required : 

(a)  For  the  sills,  which  are  to  be  8  in.  by  3  in.? 

(b)  For  the  studs,  which  are  to  be  2  in.  by  4  in.  by  18  ft., 
and  are  to  be  placed  at  intervals  of  18  in.? 

(c)  For  the  sleepers,  or  joists,  of  2  stories,  which  are  to  be 
2  in.  by  10  in.,  and  are  to  be  laid  18  in.  apart? 

(d)  For  the  plates,  which  are  to  be  4  in.  by  4  in.? 

(e)  For  the  rafters,  which  are  to  be  3  in.  by  5  in.  and  are 
to  be  1-J-  ft.  apart?     The  roof  is  to  project  2  ft.  and  the  peak  is 
to  be  10  ft.  above  the  plates. 

(/)  For  the  2  floors,  if  the  flooring  is  to  be  1J  in.  thick? 

(g)  For  the  siding  for  the  outside? 

(h)  How  many  square  feet  of  roofing  will  there  be? 

\i)  How  many  square  yards  of  plastering  will  there  be  on 
the  walls  and  ceiling  of  both  stories,  the  lower  rooms  being 
9  ft.  high,  and  the  upper  ones  7  ft.  high? 

(/)  If  the  cornice  is  to  be  2  ft.  wide,  what  will  it  cost  at 
$80  per  M? 

27.  A  cellar  22  ft.  by  34  ft.  and  9  ft.  deep  (inside  measure- 
ments) is  to  be  built. 

(a).  If  the  wall  is  to  be  20  in.  thick,  how  many  cubic  feet  of 
masonry  will  it  contain? 

(b)  How  many  cords  of  stone  will  be  required? 

(c)  How  many  loads  of  earth  must  be  removed  in  digging 
the  cellar? 

(d)  How  many  square  yards  of  plastering  will  there  be  on 
the  walls  of  the  cellar? 

(e)  How  many  square  feet  of  cement  will  there  be  on  the 
cellar  bottom? 


PERCENTAGE 

235.      OPERATIONS   WITH   HUNDREDTHS 

PROBLEMS 

1.  Find  .08  of  250;  .25  of  730;  .60  of  840. 

2.  Find  3  hundredths  of  $600 ;  12  hundredths  of  $180. 

3.  A   merchant    gained   .05   of  $1260.     How   much   did 
he  gain? 

4.  A  dealer  lost  .06  of  $790.     How  much  did  he  lose? 

5.  18  is  how  many  hundredths  of  24? 

6.  9  is  how  many  hundredths  of  36? 

7.  .05  of  a  number  is  60.     Find  the  number. 

8.  A  man  began  business  with  $1200  and  gained  .20  on  his 
investment.     How  much  had  he  then? 

9.  .15  of  a  number  is  75.     What  is  the  number? 

10.  12  is  how  many  hundredths  of  48? 

11.  17  is  how  many  hundredths  of  136? 

12.  Find  .22  of  184. 

13.  10  is  .02  of  a  number.     What  is  .01  of  the  number? 
What  is  the  number? 

H.  25  is  .04  of  a  number.     What  is  the  number? 

15.  18  is  .35  of  what  number? 

16.  What  is  .45  of  560? 

17.  A  merchant   gained  $42  on   $350.     How   many  hun- 
dredths of  his  investment  did  he  gain? 

18.  A   dealer  lost   .08   of    his    iuvescment.      How    many 
hundredths  of  his  investment  had  he  left? 

19.  A  dealer  gained  .12  of  his  capital.     How  many  hun- 
dredths of  his  original  capital  had  he  then? 

20.  $7.50  is  how  many  hundredths  of  $25? 

21.  $46.30  is  how  many  hundredths  of  $578.75? 

22.  What  is  .55  of  1125? 

23.  A  man  lost  .14  of  his  money.     How  many  hundredths 
had  he  left? 

139 


140  MODERN   COMMERCIAL   ARITHMETIC 

^4.  A  man  borrowed  $850  and  paid  .06  of  that  amount 
each  year  for  the  use  of  the  money.  How  much  did  he  pay 
each  year? 

25.  Find  43  hundredths  of  700. 

APPLICATIONS  OF  PERCENTAGE 

236.  Per  cent  means  hundredths. 

237.  In  many  business  operations  we  say  per  cent  instead 
of  hundredths.     Read  the  examples  on  the  preceding  page,  and 
read  per  cent  instead  of  hundredths.     The  meaning  will   be 
the  same. 

238.  Percentage  means  a  process  involving  hundredths,  or 
per  cent.     The  examples  on  the  preceding  page  are  examples 
in  percentage. 

239.  Operations    in    percentage  involve   certain   business 
terms,  a  certain  knowledge  of  the  way  in  which  business  is 
done,  and  decimals. 

How  Per  Cent  Is  Expressed 

240.  Since  per  cent  means  hundredths,   it  is  commonly 
expressed  as  a  decimal.     It  may  also  be  expressed  as  a  common 
fraction.     Thus,  .05  =  1|Tr  =  -fa. 

241.  The  sign  of  per  cent  is  %. 

242.  Expression  of  hundredths : 

.01=    l%=T*o-  -05=      5%=Tfo  =  *V 

.50  =  50%  =T5o°o=i.  .10=    10%  =TV°o  =TV 

.75  =  75%=TVTr  =  f.  -20=    20%=fV°o  =    t- 

.25  =  25%  =  TVo  =  i.  1.25  =  125%  =  ±U  =  H- 

.04  =    4%  =  Tfo  =  fa.  1.50  =  150%  =  f|§  =  H. 

243.  Hundredths  as  aliquot  parts: 

12|%  =  |.  33^%  =  J.  66f  %  =  |. 

16*%  =  I  37i%  =  f .  75   %  =  f . 

20  %  =  f  50   %  =  i.  87^%  =  |. 

25   %  =  i.  62|%  =  f .  125  %  =  1±. 

NOTE. — When  more  convenient,  these  fractional  parts  should  be 
used  instead  of  the  decimal  equivalents. 


PERCENTAGE  141 

244.  Some  expressions : 

*%  is  read  one-third  of  one  per  cent,  or  one-third  per  cent. 
It  is  written  decimally  .00*,  not  .*. 

8%  =  .08;  .8%  =  .008;  .08%  =  .0008;  .008%  =  .00008. 
The  sign  %  indicates  two  decimal  places. 
Adding  the  sign  %  is  equivalent  to  pointing  off  two  decimal 
places,  or  dividing  by  100. 

EXERCISES 
Express  decimally: 

1.  18%.         8.   6*%.         5.   66*%.         7.  f%.  9.     7*%. 

2.  93%.         4.  7±%.         6.  25f%.         8.  f%.          10.   .024%. 
Express  as  common  fractions : 

1.  33*%.         5.  87*%.         5.   16|%.         7.  *%.  P.  f%. 

0.  83*%.         4.   125%.         6.       |%.         *.  i%.  ^.  f%. 

Express  as  a  per  cent : 

*.  *•                  3.  *.                  5.  *.                  7.  f.  P.  A- 

0.  ±.                4.  J.                ^.  i                A  f.  *?.  TV- 

245.  An  example  in  percentage  involves: 

(a)  A  decimal  that  indicates  a  part  of  a  number. 

(b)  The  part  of  the  number  indicated  by  the  decimal. 

(c)  The  number  of  which  a  part  is  indicated. 

The  decimal  =  rate  per  cent,  or  rate 
The  part        =  percentage 
The  number  =  base 

246.  The  decimal  that  shows  how  many  hundredths  of  a 
number  are  taken  is  the  Eate  Per  Cent. 

247.  The  number  of  which  the  hundredths  are  taken  is 
the  Base. 

248.  The  number  that  is  a  given  number  of  hundredths 
of  the  base  is  the  Percentage. 

249.  When  the  percentage  is  added  to  the  base,  the  sum 
is  called  the  Amount. 

250.  When  the  percentage  is  subtracted  from  the  base, 
the  remainder  is  called  the  Difference. 


142  MODERN    COMMERCIAL   ARITHMETIC 

251.  To  Find  the  Percentage 

MENTAL  PROBLEMS 

1.  Find  i  of -36;  25%  of  36. 

2.  What  is  y1^  of  750?     10%  of  750? 

3.  What  is  .02  of  800?     2%  of  800? 

4.  What  is  33£%  of  72?  of  48?  of  60? 

5.  Find  16f  %  of  96. 

6.  Find  25%  of  28;  of  44;  of  64. 

7.  Find  62£%  of  72;  of.  144. 

8.  Find  66f%  of  15;  of  24. 

9.  Find  40%  of  250. 
10.  Find  12| %  °f  40  yd. 

FORMULA 
Base  x  rate  =  percentage 

PROBLEMS 

Find  the  percentage,  the  amount,  and  the  difference: 

1.  24%  of  360.  11.  12|%  of  840  cows. 

2.  42%  of  $700.  12.  37|%  of  944  horses. 

3.  65i%  of  $840.  13.  16f  %  of  $2563.92. 

4.  83%  of  $762.50.  14.  84%  of  4672  Ib. 

5.  29|%  of  $538.20.  15.  112£%  of  $354.62 

6.  25%  of  $684.40.  16.  108^%  of  6457. 

7.  75%  of  $932.60.  17.  125%  of  6820. 

8.  33£%  of  $638.60.  18.  35f%  of  $921.30. 

9.  87i%  of  $9734.  19.  53%  of  $749.80. 
10.  66f%  of  $1248.  20.  28%  of  4648. 

21.  A  drover  bought  780  sheep,  and  sold  30%  of  them. 
How  many  had  he  left? 

22.  A   dealer   bought   34%    of  a  stack  of  hay  containing 
18  T.  14  cwt.     How  much  hay  did  he  buy? 

28.  23-|%  of  a  barrel  of  oil  leaked  out.  If  the  barrel  held 
48  gal.,  how  much  was  lost? 

24.  How  much  lead  will  be  obtained  from  580  tons  of  ore, 
if  the  ore  yields  15%  of  metal? 


PERCENTAGE  143 

25.  If  cloth  will  shrink  4-^%,  what  will  be  the  shrinkage 
on  128  yd.? 

26.  If  .27%  of  coloring  is  to  he  mixed  with  white  paint, 
how  much  coloring  must  be  used  with  3  T.   7  cwt.  80  Ib. 
of  paint? 

27.  In  making  a  certain  medicine,  .04%  of  arsenic  is  used. 
How  much  arsenic  will  be   used  in  making   420  Ib.  of   the 
medicine? 

252.  To  Find  the  Bate 

MENTAL  PROBLEMS 

1.  8  is  what  part  of  100?     20  is  what  part  of  100? 

2.  Of  100,  15  is  what  part?     35?     17?   82? 
8.  4  is  what  part  of  5?     7  of  9?     8  of  15? 

4.  4  is  how  many  hundredths  of  5?  3  of  4?  4  of  16? 

5.  4  is  what  per  cent  of  5?  of  8?  of  16?  of  32? 

6.  8  is  what  per  cent  of  16?  of  24?  of  12? 

7.  6  is  what  per  cent  of  12?  of  24?  of  18? 

8.  9  is  what  per  cent  of  18?  of  27?  of  36? 

9.  12  is  what  per  cent  of  24?  of  18?  of  36?  of  60? 

10.  What  per  cent  of  44  is  11?  22?  33? 

11.  What  per  cent'  of  60  is  15?  12?  20?  30?  45? 

12.  What  per  cent  of  4  is  f  ?  |?  f  ?  4? 

FORMULA 
P  (percentage)  =  E  (rate)  x  B  (base) 


PROBLEMS 

1.  What  per  cent  of  270  is  90? 

2.  What  per  cent  of  38  is  27? 

3.  45  is  what  per  cent  of  60? 

4.  Of  165,  15  is  what  per  cent? 

5.  What  per  cent  of  $860  is  $520? 

6.  $750  is  what  per  cent  of  $500? 

7.  140  sheep  are  what  per  cent  of  560  sheep? 

8.  What  per  cent  of  $900  is  $1200? 


144  MODERN    COMMERCIAL   ARITHMETIC 

9.  3465  is  what  per  cent  of  4587? 

10.  What  per  cent  of  860000  is  580? 

11.  What  per  cent  of  720  is  24000? 

12.  480000  is  what  per  cent  of  12000000? 

13.  T5T  is  what  per  cent  of  T\? 

14.  What  per  cent  of  .86  is  .32? 

15.  What  per  cent  of  6.25  is  98.75? 

16.  The  United  States  silver  dollar  weighs  26.729  gr,,  and 
the  Japanese  dollar  weighs  26.9564  gr.     The  weight  of  the 
American  dollar  is  what  per  cent  of  the  weight  of  the  Japanese 
dollar? 

17.  A  hank  has  $257326  cash  on  hand,  and  its  deposits  are 
$10658730.     The  bank  report  will  state  that  the  cash  on  hand 
is  what  per  cent  of  the  deposits? 

18.  A  bank  has  received  $14873580,  and  can  repay  only 
$3672500.     What  will  a  man  receive  who  has  deposited  $1260? 

19.  The  following  table  shows  the  population  and  number 
of  deaths  for  a  period  of  time  in  three  cities : 

POPULATION  NUMBER  OF  DEATHS 
2768000  138 

1875000  116 

2162000  154 

Find  the  death  rate  (per  cent)  for  each  city. 

20.  Three  substances  are  mixed  in  the  proportion  of  5,  21, 
and  38.     Each  substance  is  what  per  cent  of  the  mixture?    How 
many  pounds  of  the  first  substance  in  85  Ib.  of  the  mixture? 

21.  In  a  school  of  55  pupils,  there  were  16  absences  in  10 
days.     What  was  the  rate  per  cent  of  attendance? 

22.  If  out  of  76000000  passengers  420  are  killed,  what  per 
cent  of  the  passengers  are  killed? 

23.  If  a  bushel  of  apples  weighs  50  Ib.,  and  10  bu.  of  apples 
will  make  32  gal.  of  cider  weighing  8£  Ib.  per  gallon,  what  per 
cent  of  the  apples  becomes  cider? 

24.  From  a  substance  weighing  8  Ib.  4  oz.  (Troy),  7  dr.  of 
a  mineral  were  obtained.     What  per  cent  of  mineral  did  the 
substance  yield? 


PERCENTAGE  145 


353.  To  Find  the  Base 

MENTAL  PROBLEMS 

1.  25  is  £  of  what  number? 

2.  25  is  20%  of  what  number? 

3.  30  is  33£%  of  what  number? 

4.  16  is  8%  of  what  number? 

5.  12  is  40%  of  what  number? 

6.  Of  what  number  is  12  60%? 

7.  15  is  75%  of  what  number? 

8.  Of  what  number  is  14  7%? 

9.  Of  what  number  is  20  40%? 

10.  Of  what  number  is  25  37|%? 

11.  Find  the  number  of  which  20  is  20%. 

12.  Find  the  number  of  which  40  is  5%. 

13.  Find  the  number  of  which  60  is  12%. 

14.  Of  what  number  is  18  6%? 

15.  Of  what  number  is  27  33£%? 

16.  100  is  12|%  of  what  number? 

17.  32  is  62i%  of  what  number? 

18.  72  is  9%  of  what  number? 

FORMULA 


PROBLEMS 

1.  Find  the  number  of  which  10608  is  17%. 

2.  $43.40  is  32%  of  what  sum? 

3.  472  is  33£%  of  what  number? 

4.  f  is  40%  of  what  number? 

5.  Of  what  number  is  675  16f  %? 

6.  Of  what  number  is  924  .056%? 

7.  Of  what  number  is  87  •£%? 

8.  Find  the  number  of  which  3.045  is  24£%. 

9.  .0000315  is  .08£%  of  what  number? 

10.  Find  the  number  of  which  530100  is  .57%. 

11.  A  business  pays  a  net  gain  of  $2865  per  annum.     A 
buyer  offers  for  the  business  a  sum  of  which  the  net  gain  shall 
be  8%.     What  is  the  value  of  his  offer? 


146  MODERN    COMMERCIAL   ARITHMETIC 

12.  A  company  with  a  capital  of  $685750  pays  annual  divi- 
dends to  the  amount  of  444573.75.  The  next  year  the  dividends 
are  $76242.30,  and  the  company  wish  to  report  a  capitalized 
value  of  their  business  that  shall  yield  the  same  per  cent  of 
dividends  as  did  the  capital  the  year  before.     What  will  be  the 
reported  capital  of  the  company  the  second  year? 

13.  A  mine  pays   $623750  annually.      If  invested  money 
pays  on  an  average  4£%  of  itself  as  profits,  what  is  the  cash 
value  of  the  mine? 

H.  A  certain  business  pays  5%  dividends.  How  much 
must  be  invested  in  the  business  to  produce  an  annual  income 
of  $1375? 

15.  If  wine  contains  11  J%  of  alcohol,  how  much  wine  must 
be  purchased  by  a  distiller  who  wishes  to  make  586  gal.  of 
alcohol  from  the  wine? 

16.  If  a  certain  paint  contains  .7%  of  zinc,  how  much  paint 
can  be  made  from  200  Ib.  of  zinc? 

17.  A  solution   contains  .003%   of   arsenic.      How   many 
grains  of  the  solution  must  be  taken  to  get  12  gr.  of  arsenic? 

18.  If  an  agent  receives  3%  commission  for  selling  goods, 
how  many  goods  must  he  sell  to  earn  $275? 

19.  A  manufacturer  wishes  to  make  a  composition  metal  to 
consist  of  3S%    of  gold,   5%   of  silver,   4%   of  tin,  and  the 
remainder  copper.     If  he  has  120  Ib.  (Troy)  of  gold,  how  much 
of  each  of  the  other  metals  must  he  add  to  it? 

20.  A  custom  miller  takes  8%  of  the  grist  for  grinding. 
How  many  pounds  of  oats  must  be  taken  to  the  mill  to  get  300 
Ib.  of  feed? 

254:.  To  Find  the  Amount  and  Base 

MENTAL  PROBLEMS 

1.  10  is  what  per  cent  of  10? 

2.  Any  number  is  what  per  cent  of  itself? 

3.  The  base  is  always  what  per  cent  of  itself? 

4.  The  percentage  is  what  of  the  base? 

5.  What  is  the  base  plus  the  percentage  called? 

6.  What  is  100%  plus  the  rate  per  cent  called? 


PEKCENTAGE  147 

7.  If  the  rate  is  8%,  what  is  the  amount  per  cent? 

8.  If  the  base  is  100  and  the  rate  8%,  what  is  the  amount? 
«?.  The  amount  in  the  last  question  is  what  per  cent  of  the 

base? 

10.  If  the  amount  per  cent  is  110%,  what  per  cent  is  the 
base? 

11.  If  the  amount  is  110  and  the  amount  per  cent  is  110%. 
what  is  the  base? 

12.  If  the  amount  per  cent  is  115%  and  the  base  is  300, 
what  is  the  amount? 

13.  If  the  amount  per  cent  is  115%  and  the  amount  is  345, 
what  is  the  base? 

14.  If  the  amount  per  cent  is  107%  and  the  base  is  400, 
what  is  the  amount? 

15.  If  the  amount  per  cent  is  107%  and  the  amount  is  428, 
what  is  the  base? 

16.  If  the  rate  per  cent  is  5  %  and  the  base  is  600,  what  is 
the  amount? 

17.  If  the  rate  per  cent  is  5%  and  the  amount  is  630,  what 
is  the  base? 

FORMULA 

B  -f  percentage  =  amount 
100%  +  rate  per  cent  =  amount  per  cent 
Base  x  amount  per  cent  =  amount 
Amount  -f-  amount  per  cent  =  base 

PROBLEMS 
Find  the  base : 

1.  When  the  amount  per  cent  is  112^  and  the  amount  is 
1000. 

2.  When  the  amount  is  1680  and  the  amount  per  cent  is  105. 

3.  When  the  amount  is  $29.38  and  the  amount  per  cent  is 
113. 

4-  When  the  amount  per  cent  is  103  and  the  amount  is  460. 
5.  When  the  amount  per  cent  is  102^  and  the  amount  is 
65.83. 


148  MODERN    COMMERCIAL   ARITHMETIC 

6.  When  the  amount  is  $1268  and  the  rate  per  cent  is  4. 

7.  When  the  rate  is  12^-%  and  the  amount  is  $1475.65. 

8.  When  the  amount  is  763  and  the  amount  per  cent  is 
100.7. 

9.  When  the  amount  is  $528.25  and  the  rate  is  12|%. 

10.  WThen  the  rate  is  .06£%  and  the  amount  is  $1194.50. 

11.  What  number  increased  by  25%  of  itself  is  855? 

12.  If  it  costs  3%  of  the  price  of  iron  to  buy  it,  how  much 
iron  can  be  bought  for  $1648? 

IS.  If  a  jeweler  adds  to  gold  an  alloy  equal  to  21%  of  the 
weight  of  the  gold,  how  much  pure  gold  must  be  used  in  mak- 
ing 31  Ib.  (Troy)  of  the  alloyed  gold? 

14.  If  metal  bars  will  expand  -J %   when  heated,  how  long 
should  they  be  made  if,  after  expanding,  they  should  be  18  ft. 
long? 

15.  If  a  business  pays  8%  per  annum,  how  much  must  a 
man  invest  in  the  business  so  that  at  the  end  of  the  year  his 
interest  in  the  business  shall  be  worth  $10000? 


255.  To  Find  the  Difference  and  Base 

MENTAL  PROBLEMS 

1.  What  is  the  base  less  the  percentage  called? 

NOTE. — 100%  less  the  rate  per  cent  is  called  the  Difference  Per 
Cent. 

2.  If  the  rate  is  8%,  what  is  the  difference  per  cent? 

3.  If  the  base  is  100  and  the  rate  is  8%,  what  is  the  differ- 
ence? 

4.  In  the  above  example,  the  difference  is  what  per  cent  of 
the  base? 

5.  If  the  difference  per  cent  is  90%   and  the  base  is  100, 
what  is  the  difference? 

6.  If  the  difference  is  90,  and  the  difference  per  cent  is  90%, 
what  is  the  base? 

7.  If  the  difference  per  cent  is  85%  and  the  base  is  300, 
what  is  the  difference? 


PEKCEKTAGE  149 

8.  If  the  difference  "per  cent  is  85%  and  the  difference  is 
255,  what  is  the  base? 

9.  If  the  difference  per  cent  is  95%   and  the  base  is  400, 
what  is  the  difference? 

10.  If  the  difference  per  cent  is  95%  and  the  difference  is 
380,  what  is  the  base? 

11.  If   the  rate  is  6%   and  the  base  is  600,  what  is  the 
difference? 

12.  If  the  rate  is  6%  and  the  difference  is  564,  what  is  the 
base? 

FORMULAE 

100%  -  rate  per  cent  =  difference  per  cent 
Base  —  percentage  =  difference 
Base  x  difference  per  cent  =  difference 
Difference  -*-  difference  per  cent  =  base 


PROBLEMS 
Find  the  base : 

1.  When  the  difference  per  cent  is  92  and  the  difference  is 
1656. 

2.  When  the  difference  is  $245  and  the  difference  per  cent 
is  86. 

3.  When  the  difference  is  750  and  the  rate  is  15%. 

4.  When  the  rate  is  12|  per  cent  and  the  difference  is  $435. 

5.  When  the  difference  per  cent  is  79  and  the  difference  is 
$692.40. 

6.  When  the  difference  is  804  and  the  difference  per  cent 
is  67. 

7.  When  the  rate  is  6£%  and  the  difference  is  $379.25. 

8.  When  the  difference  is  $119.36  and  the  difference  per 
cent  is  97.25. 

9.  When  the  rate  is  .0036  and  the  difference  is  $274.86. 

10.  What  number  diminished  by  13%  of  itself  equals  1827? 

11.  If  the  waste  in  melting  a  metal  and  making  it  into 
articles  is  2£%,  how  much  metal  must  be  used  to  make  1865 
Ib.  of  the  articles? 


150  MODERN    COMMERCIAL   ARITHMETIC 

12.  If  cloth,  shrinks  3%  in  length  "and  a  man  wishes  to  use 
a  piece  136  yd.  long  after  shrinking,  how  much  cloth  must  he 
buy? 

18.  How  many  pounds  of  alloyed  gold  must  be  taken  to 
obtain  86  Ib.  of  pure  gold  if  it  contains  22 %%  of  alloy? 

14-  A  customer  ordered  380  of  a  certain  article,  and 
remitted  money  enough  to  pay  for  them,  with  instructions  to 
send  as  many  articles  as  the  money  would  buy  in  case  there 
should  be  any  discount  on  the  goods.  If  a  discount  of  5% 
is  allowed,  how  many  articles  should  be  sent  him? 

15.  If  it  costs  3%  of  the  price  of  goods  to  sell  them,  how 
many  goods  must  be  sold  to  net  the  dealer  $1000? 

PROFIT  AND  LOSS 

QUESTIONS 

256.  1.  Are  goods  ever  sold  at  a  loss  to  the  dealer? 

2.  Show  how  each  of  the  following  may  cause  a  dealer  to 
sell  below  cost:  fire,  flood,  competition,  out-of-style  goods,  lack 
of  storage,  desire  to  advertise,  supply  of  perishable  goods. 

NOTE.— The  rate  of  gain  or  loss  is  usually  computed  as  a  per  cent. 

S.  Comparing  the  terms  of  percentage  with  those  of  profit 
and  loss,  to  what  does  the  cost  (to  the  dealer)  compare?  The 
whole  gain  or  loss  corresponds  to  what  term  in  percentage? 
The  per  cent  of  profit  or  loss?  The  selling  price  if  at  a  gain? 
The  selling  price  if  at  a  loss? 

MENTAL  PROBLEMS 

1.  Sold  a  hat  that  cost  $2  at  a  gain  of  20%.    What  was  the 
gain?     What  was  the  selling  price? 

2.  Sold  a  cow  that  cost  $24  at  a  gain  of  12|%.     What  was 
the  gain?     The  selling  price? 

8.  Sold  an  article  that  cost  $30  at  a  loss  of  33£%.  What 
was  the  loss?  The  selling  price? 

4.  Sold  an  article  that  cost  $50  at  a  gain  of  15%.  What 
was  the  gain?  The  selling  price? 


PERCENTAGE  151 

5.  Bought  a  book  for  $2  and  sold  it  for  $3.     How  much 
was  gained?     What  per  cent  of  the  purchase  price  was  gained? 

6.  Bought  a  watch  for  $12  and  sold  it  for  $16.     How  much 
was  gained?     What  part  of  the  purchase  price  was  gained? 
What  was  the  gain  per  cent? 

7.  Gain  or  loss  is  reckoned  at  a  certain  per  cent  of  what 
sum?    • 

8.  Bought  a  horse  for  $50  and  sold  it  for  $40.     How  much 
was  lost?     What  part  of  the  cost  was  lost?     What  was  the  loss 
per  cent? 

9.  If  an  article  costs  $2.40,  for  how  much  must  it  be  sold  to 
gain  25%? 

10.  A  man  bought  a  wagon  for  $45  and  paid  $15  for  repairs. 
If  he  then  sold  the  wagon  for  $70,  what  was  his  gain  per  cent? 

11.  If  you  buy  a  book  for  $2. 60  and  know  that  the  dealer 
made  a  profit  of  30%,  how  much  did  the  book  cost  the  dealer? 

12.  At  what  price  must  an  article  be  bought  so  that  it  may 
be  sold  for  $2.80  and  make  a  profit  of  40%? 

IS.  A  man  wishes  to  sell  shoes  for  $2.50  and  make  a  profit 
of  25%.     What  is  the  most  he  can  afford  to  pay  for  the  shoes? 

14.  A  shoe  dealer  who  sells  at  a  profit  of  20%  made  $1200. 
What  did  he  pay  for  the  goods  sold?     What  did  he  sell  them 
for? 

15.  If  you  know  that  a  dealer  makes  $60  on  the  sale  of  a 
piano,  and  that  he  sells  at  a  profit  of  15%,  you  know  that  the 
piano  cost  him  how  much? 

16.  If  an  article  is  marked  $4.80  and  you  know  that  the 
dealer  makes  a  profit  of  20%,  you  know  that  the  article  cost 
him  how  much? 

17.  If  an  article  cost  $1.50,  how  must  it  be  marked  to 
insure  a  gain  of  30%? 

18.  A  merchant  buys  eggs  at  12^  per  dozen  and  sells  them 
at  14^  per  dozen.     What  per  cent  does  he  gain? 

19.  Bought  an  article  for  £  its  list  price,  and  sold  it  for  f 
its  list  price.     What  per  cent  was  gained? 

20.  Bought  an  article  for  $24  and  sold  it  for  $20.     What 
was  the  per  cent  of  loss? 


152 


MODERN    COMMERCIAL    ARITHMETIC 


21.  If  an  article  is  bought  for  $8  and  sold  at  a  loss  of 
what  is  the  selling  price? 

22.  If  an  article  is  bought  20%  below  cost  and  sold  20% 
above  cost,  what  is  the  gain  per  cent  on  the  investment? 


TABLE    FOR   MENTAL   DRILL 


GAIN  % 

GAIN 

Loss  % 

Loss 

SELLING 
PRICE 

P  URCHASE 

PRICE 

1 

10 

$20 

9 

9 

2 

? 

$15 

$75 

? 

3 

12^- 

9 

9 

$200 

4 
5 

5 

$25 
9 

$18 

9 

$  20 

6 

9 

9 

$20 

$  18 

7 

8 

9 

9 

$     1.20 

8 

10 

9 

$90 

9 

9 

? 

$12 

$92 

? 

10 

14 

? 

$  5.70 

? 

11 

15 

$  4.50 

9 

9 

12 

20 

9 

9 

$     6.50 

13 

7 

9 

? 

$  14 

14 

33i 

$25 

9 

? 

15 

6 

9 

? 

$     1.20 

16 

? 

$24 

$96 

9 

17 

12 

? 

9 

$  15 

18 

9 

$12 

9 

$  42 

19 

10 

$22 

? 

9 

20 

? 

$  6 

$48 

? 

21 

16 

9 

$23.20 

9 

22 

15 

? 

$17 

9 

23 

9 

$  3 

9 

$  18 

n 

37| 

$40 

9 

9 

PROBLEMS 

1.  For  how  much  must  goods  that  cost  $875.38  be  sold  so 
as  to  gain  21|%? 

2.  A  merchant  bought  dishes  for  $1.15  per  dozen.     At  what 
price  must  he  sell  them  apiece  to  gain  20%? 

3.  A  dealer  bought  wheat  at  98^  per  bushel  and  sold  it  at 
$1.10  per  bushel.     What  per  cent  did  he  gain? 


PERCENTAGE  153 

4.  If  a  man  buy  2400  brick  for  $8,  for  how  much  per  M 
must  he  sell  them  to  gain  15%? 

5.  On  an    investment  of    $2875  a   man    gained    $213.50. 
What  was  his  gain  per  cent? 

6.  Jan.  1,  1897,  a  man  invested  $3800.     Jan.  1,  1900,  his 
investment  was  worth  $4425.     What  was  his  gain  per  cent  per 
annum? 

7.  A  furniture  dealer  sold  furniture  that  cost  him  $1125, 
at  12£%  below  cost.     What  was  his  loss? 

8.  If  a  horse  is  bought  for  $85  and  sold  for  $75,  what  is  the 
loss  per  cent? 

9.  A  man  invested  $1680  and  afterward  sold  his  investment 
for  $1475.     What  was  his  loss  per  cent? 

10.  A  grocer  bought  a  barrel  of  sugar  containing  420  Ib. 
for  $16.     What  will  be  his  gain  per  cent  if  he  sells  it  at  50  per 
pound? 

11.  A  grocer  bought  64  Ib.  of  ginger  for  $12.80.     For  how 
much  per  pound  must  he  sell  it  to  gain  25%? 

12.  A  produce  dealer  bought  250  bu.  of  wheat  at  850  per 
bushel,  360  bu.  of  oats  at  320  per  bushel,  415  bu.  of  corn  at 
280  per  bushel,  and  16  bu.  of  beans  at  $1.80  per  bushel.     If 
he  sold  the  wheat  at  900  per  bushel,  the  oats  at  300  per  bushel, 
the  corn  at  300  per  bushel,  and  the  beans  at  $1.95  per  bushel, 
what  was  his  entire  gain  per  cent? 

13.  A  real  estate  dealer  bought  a  lot  for  $2600  and  paid 
$85  for  a  fence,  $30  for  digging  a  drain,  $160  for  street  repair, 
and  $3250  for  a  house.     For  how  much  must  he  sell  the  house 
and  lot  to  gain  15%  on  his  investment? 

H.  A  druggist  bought  alcohol  at  $2  per  gallon  and  sold  it 
at  350  per  pint.     What  was  his  gain  per  cent? 

15.  If  collars  are  bought  for  $1.10  per  dozen  and  sold  at  150 
apiece,  what  is  the  gain  per  cent? 

16.  If  plates  must  be  sold  at  200  apiece,  for  how  much 
must  they  be  purchased  to  insure  a  gain  of  20%? 

17.  A  fruit  dealer  bought  200  pineapples  at  7f  apiece.     13 
of  them  spoiled,  and  he  sold  the  remainder  at  80  apiece.     What 
was  his  gain  per  cent? 


154  MODERN    COMMERCIAL   ARITHMETIC 

18.  A  dealer  lost  £  of  a  load  of  fruit.     At  what  per  cent  of 
profit  must  the  rest  be  sold  that  he  may  gain  20%   on  the 
whole  load? 

19.  Bought  a  farm  of  260  acres  for  $28  per  acre,  and  paid 
$320  for  fencing,  $850  for  repairs,  $175  for  draining,  $82  for 
taxes.     At  what  price  per  acre  must  it  be  sold  to  gain  20%  on 
the  investment? 

20.  If  shoes  are  bought  for  $3  per  pair,  how  must  they  be 
marked  that  the  dealer  may  make  a  reduction  of  10%  from  the 
marked  price  and  gain  20%  on  the  cost? 

21.  What  per  cent  is  gained  on  goods  marked  30%  above 
cost  and  sold  at  20%  off  from  the  marked  price? 

22.  What  is  the  gain  or  loss  per  cent  on  goods  marked  25% 
above  cost  and  sold  at  25%  off  from  the  marked  price? 

28.  It  costs  a  publishing  house  $1.64  to  produce  a  book. 
If  the  house  wishes  to  make  a  profit  of  25%  on  the  first  cost  of 
the  book,  and  allows  the  agents  40%  of  the  sales  of  the  book, 
at  what  price  must  the  house  have  the  agents  sell  the  book? 

24.  At  what  price  per  dozen  must  caps  be  bought  that  the 
dealer  may  sell  them  at  30^  apiece  and  gain  20%? 

MENTAL  EXERCISES 
Tell  how: 

1.  To  find  the  gain  when  the  cost  and  per  cent  of  gain  are 
given. 

2.  To  find  the  gain  per  cent  when  the  cost  and  selling  price 
are  given. 

3.  To  find  the  gain  per  cent  when  the  gain  and  selling  price 
are  given. 

4.  To  find  the  gain  per  cent  when  the  gain  and  cost  are 
given. 

5.  To  find  the  loss  when  the  cost  and  per  cent  of  loss  are 
given. 

6.  To  find  the  loss  per  cent  when  the  cost  and  selling  price 
are  given. 

7.  To  find  the  loss  per  cent  when  the  loss  and  cost  are 
given. 


PERCENTAGE  155 

8.  To  find  the  loss  per  cent  when  the  loss  and  selling  price 
are  given. 

9.  To  find  the  selling  price  when  the  gain  and  per  cent  of 
gain  are  given. 

10.  To  find  the  selling  price,  the  loss  and  loss  per  cent 
being  given. 

11.  To  find  the  cost,  the  gain  and  gain  per  cent  being 
given. 

12.  To  find  the  cost,  the  loss  and  loss  per  cent  being  given. 
18.  To  find  the  cost,  the  selling  price  and  gain  per  cent 

being  given. 

14-  To  find  the  cost,  the  selling  price  and  loss  per  cent 
being  given. 

COMMISSION   AND   BROKERAGE 

257.  A  person  who  does  business  for  another  is  an  Agent. 

The  book  agent  sells  books  for  the  publisher.  The  clerk  in 
a  store  sells  merchandise  for  his  employer.  The  traveling 
salesman  takes  orders  for  goods  to  be  filled  by  his  house.  A 
commission  merchant  resides  in  some  city  and  receives  goods 
to  be  sold  by  him.  A  man  in  New  York  may  receive  farm  prod- 
uce from  a  farmer,  sell  the  stuif  at  the  market  price,  take  out 
his  charges,  and  remit  the  balance  to  the  farmer.  A  broker 
buys  and  sells  bonds,  stock  certificates,  etc.,  for  others. 

Some  agents  receive  a  salary.  Some  receive  a  percentage 
on  the  things  they  buy  or  sell. 

258*  The  pay  that  an  agent  receives  is  called  Commission. 

259*  The  pay  a  broker  receives  is  called  Brokerage. 

260.  The  agent's  commission  is  computed  on  what  he  buys 
or  sells. 

261.  The  person  for  whom  the  agent  transacts  business  is 
the  Principal.     A  company,  firm,  or  corporation  is  considered 
in  business  as  a  person. 

262.  Goods  sent  by  a  principal  to  an  agent  is  a  Consign- 
ment. 

263.  The  principal    is  the  Consignor,  the  agent  is  the 
Consignee. 


156  MODEKN"    COMMERCIAL   ARITHMETIC 

264.  For  taking  the  risk  of  loss  from  sales  on  credit  or  for 
pledging  the  quality  of  the  goods  bought,  the  agent  makes  a 
charge  called  Guaranty. 

265.  The  charges  that  an  agent  may  make  to  his  principal 
are  commission,  guaranty,  freight,  storage,  insurance,  inspec- 
tion, etc. 

266.  The  whole  amount  received  by  an  agent  from  a  sale 
or  a  collection  is  the  Gross  Proceeds. 

267.  The  sum  that  remains  after  the  agent  has  deducted 
all  his  charges  is  the  Net  Proceeds. 

268.  Sometimes  a  principal  sends  to  his  buying  agent  a 
sum  of  money  (remittance)  that  includes  the  agent's  commis- 
sion and'  the  sum  to  be  invested.     The  agent  is  to  invest  as 
much  as  he  can  and  still  have  enough  left  for  his  commission. 

269.  The  sum  actually  invested  in  goods  is  the  Prime  Cost, 
or  Net  Cost.     The  net  cost  -»lus  all  charges  of  the  agent  is  the 
Gross  Cost. 

270.  Comparing  the  terms  of  commission  and  brokerage 
with  the  terms  of  percentage : 

The  gross  proceeds  =  ? 
The  net  cost  =  ? 
The  rate  of  commission  =  ? 
The  commission  =  ? 

Purchase  price  +  commission,  or   remittance   to  agent  for 
investment  =  ? 

Selling  price  —  commission  =  ? 


271.     To  Compute  Commission  and  Brokerage 

MENTAL  PROBLEMS 

1.  An  agent  receives  40%  commission  on  his  sales.     If  he 
sells  and  delivers  $200  worth  of  books,  how  much  does  he  keep 
for  his  commission? 

2.  If  an  agent  sold  $2500  worth  of  goods  on  10%  commis- 
sion, how  much  commission  did  he  receive?     How  much  did 
he  send  to  his  principal? 


PERCENTAGE  157 

3.  An  agent  receives  12|%  commission  on  all  the  goods  he 
sells.     How  many  dollars'  worth  of  goods  must  he  sell  to  earn 
$100? 

4.  If  a  buying  agent  receives  5%   commission  for  buying 
cotton,  how  much  money  must  his  principal  send  him  to  pay 
for  $1  worth  of  cotton  and  the  commission?     If  the  principal 
sends  $5.25  to  pay  for  cotton  and  the  agent's  commission,  how 
much  cotton  will  the  agent  buy?     If  the  agent  receives  a  remit- 
tance of  $1050,  how  many  dollars'  worth  of  cotton  will  he  send 
his  principal? 

5.  If  an  agent  receives  3%  commission  for  buying  wool, 
what  does  $1  worth  of  wool  cost  the  principal?     How  much 
must  the  principal  send  the  agent  to  pay  in  full  for  $100  worth 
of  wool?     If  the  principal  remits  $206,  how  much  wool  will  he 
receive? 

6.  If  an  agent's  commission  is  2%  on  all  goods  bought,  how 
much  will  $2  worth  of  goods  cost  the  principal?     This  cost  is 
what  per  cent  of  the  purchase  price  of  the  goods? 

7.  A  farmer  sent  a  commission  merchant  500  bu.  of  wheat 
to  be  sold  on  a  commission  of  2%.     If  the  wheat  is  sold  at  80^ 
per  bushel,  how  much  should  the  farmer  receive? 

8.  If  an  agent  charges  2%  commission  for  buying  silk,  how 
much  money  must  the  principal  send  to  pay  in  full  for  $500 
worth  of  silk? 

9.  If  a  collector  receives  1%  for  collecting,  how  much  must 
he  collect  to  earn  $200  per  month?      The  principal  receives 
what  per  cent  of  the  sum  collected? 

10.  If  an  agent's  commission  for  buying  flax  is  4%,  what  per 
cent  of  the  sum  to  be  invested  in  flax  must  the  principal  send 
the  agent? 

11.  How  much  does  an  agent  earn  who  sells  $3000  worth  of 
goods  on  a  commission  of   7%?      What  sum  does  the  principal 
receive?     What  per  cent  of  the  sales  does  he  receive? 

12.  What  will  $1100  worth  of  goods  cost  a  principal,  if  he 
pays  his  agent  6%  commission?     What  per  cent  of  $1100  will 
the  goods  cost  the  principal? 

13.  How  many  dollars'  worth  of  goods  must  an  agent  sell 


158  MODERN    COMMERCIAL   ARITHMETIC 

to  earn  $160,  if  his  commission  is  4%?  If  the  principal  wishes 
to  receive  $192  as  a  result  of  the  sale,  how  many  dollars'  worth 
of  goods  must  he  send  the  agent? 

14.  If  the  agent's  commission  is  2%  for  buying,  the  prin- 
cipal must  send  the  agent  what  per  cent  of  the  value  of  the 
goods  the  principal  wishes  to  receive?     If  the  principal  wishes 
to  receive  $100  worth  of  goods,  how  much  money  must  he  send 
the  agent?     If  the  principal  sends  the  agent  $500,  how  many 
dollars'  worth  of  goods  will  he  receive? 

15.  If   the   agent's    commission    for    buying  is   3%,   how 
many  dollars'  worth  of  goods  will  $412  secure  the  principal? 

PROBLEMS 

Find  the  commission,  guaranty,  and  the  gross  cost: 

1.  Purchase  price  $875.60,  rate  of  commission  2^%. 

2.  Prime  cost  $954,  rate  of  commission  3£%. 

3.  360  bu.  wheat  at  900,  commission  2£%,  guaranty  £%. 

4.  684  bbl.  apples  at  $1.85,  commission  3%,  guaranty  1%. 

5.  Prime  cost  $1287.50,  commission  5|%,  guaranty  l-J-%, 
insurance  1%,  freight  $8.25. 

6.  17685  ft.  oak  at  $28.50  per  M,  commission  7%,  guar- 
anty 1%. 

7.  345   bbl.  flour   at   $5.80,  commission  250   per  barrel, 
.guaranty  2%. 

8.  72860  Ib.  hay  at  $12  per  ton,  commission  3%,  guaranty 
2%,  charges  37-J-^  per  ton. 

9.  127  yd.  carpet  at  $2.40,  commission  3%. 
Find  the  commission,  guaranty,  and  net  proceeds: 

10.  Gross  proceeds  $867.25,  commission  3^%. 

11.  Sold  215  bu.  corn  at  450,  commission  2-J% ,  guaranty  £% . 

12.  11680  Ib.    hay  at  $11   per  ton,   commission  2%,  guar- 
anty £%. 

13.  75600  ft.  cherry  at  $41  per  M,  commission  4%. 

14.  Gross  proceeds  $1825.30,commission  5%,  guaranty  1%%. 

15.  1625  books  at  $3.75,  commission  25%,  charges  50  per 
volume. 


PERCENTAGE  159 

16.  Gross  proceeds  $2368,  commission  22%,  guaranty  3%. 

17.  Gross    proceeds    $736.80,   commission  18%,   guaranty 
,  freight  $45,  insurance  $6.50. 

18.  65  T.  coal  at  $5.25,  commission  5%,  guaranty  1%. 
Find  the  prime  or  net  cost: 

19.  Gross  cost  $2838.71,  commission  7%. 

20.  Commission  $365.25,  rate  of  commission  2^%. 

21.  Gross  cost  $723,  commission  6%,  guaranty  1%,  freight 
$15. 

22.  Gross  cost  $1235.40,  commission  8%,  guaranty  2%. 

23.  Commission  $117.30,  rate  of  commission  4%. 

24.  Guaranty  $213.75,  rate  of  guaranty  3%. 

25.  Gross  cost  $6872,  commission  12|%,  guaranty  2%%. 

26.  Total  charges  $157.25,  commission  5%,  guaranty  1%, 
freight  $12.15. 

27.  Gross  cost  $1673.20,  commission  and  guaranty  14%. 

28.  Commission  $275,  rate  of  commission  2^%. 

29.  Guaranty  $218,  rate  of  guaranty  3%. 

SO.  Total  charges  $753,  commission  4%,  freight  $27. 

31.  Commission  $513,  rate  of  commission  9%. 
Find  the  rate  of  commission : 

32.  Commission  $412,  gross  proceeds  $13800. 

33.  Commission  $357,  net  proceeds  $6783. 
84.  Guaranty  $47,  gross  proceeds  $1342.86. 

35.  Guaranty  $195,  net  proceeds  $2705. 

36.  An  agent  sold  $4682  worth  of  goods  on  8%  commis- 
sion.    He  charged  1%  for  guaranty  and  $27  for  expenses.    Find 
the  commission,  guaranty,  and  net  proceeds. 

37.  An  agent  bought  $5387  worth  of  goods  on  13%  com- 
mission.    He  charged  2%  for  guaranty  and  $125  for  expenses. 
Find  the  gross  cost. 

38.  A  principal  sent  his  agent  $2965  to  invest  in  lace,  tak- 
ing out  commission  and  expenses.     If  the  commission  was  6% 
and  the  expenses  $17,  how  much  lace  did  the  principal  receive? 

39.  A  real  estate  agent  sold  a  farm  for  $12825  on  a  com- 
mission of  3%,  and  the  stock  on  the  farm  for  $2360  on  a  com- 
mission of  4%.     Find  the  commission. 


160  MODERN    COMMERCIAL    ARITHMETIC 

40.  A  principal  sent  his  agent  $1475,  with  instructions  to 
invest  it  in  oil.     If  his  commission  is  4%,  how  much  oil  will  he 
purchase? 

41.  How  many  dollars'  worth  of  merchandise  can  be  pur- 
chased for  $3691,  if  the  agent's  commission  is  5%? 

J$.  A  commission  merchant  received  a  consignment  of  831 
bbl.  of  flour  to  sell  on  a  commission  of  4%.  He  sells  the  flour 
at  $7. 30  per  barrel  and  pays  $14.50  for  cartage.  How  much 
should  he  remit  his  principal? 

4B.  An  agent  received  $2935  to  invest  in  wool,  taking  out 
his  commission  of  3^%.  How  much  commission  did  he 
receive? 

44-  An  agent  bought  28735  bu.  of  corn  at  45^  per  bushel, 
on  a  commission  of  1|%.  If  he  paid  $793.28  for  freight,  $112 
for  storage,  and  $41  for  cartage,  how  much  should  he  receive 
from  his  principal? 

45.  One  agent  charged  $72  for  selling  a  lot  for  $2400,  and 
another  agent  charged  3^%  commission  for  selling  a  lot  valued 
at  $2700.  Which  agent  charged  the  higher  rate  of  commission? 


TEADE   DISCOUNT 

272.  Manufacturers  and  dealers  issue  catalogues  and  cir- 
culars containing  a  description  of  their  goods  and  a  price  list. 
The  List  Price  is  the  price  given  in  the  catalogue  or  circular. 
Dealers  often  sell  for  less  than  the  list  price.  What  the  dealer 
"throws  off"  is  the  Trade  Discount.  The  list  price  may  be  put 
high  enough  so  that  the  dealer  can  allow  a  discount  and  yet 
make  a  desired  profit.  A  purchaser  is  pleased  to  buy  goods  at 
a  discount. 

Sometimes,  after  getting  out  a  price  list,  the  market  price 
of  goods  falls,  and  instead  of  changing  the  price  list  the  dealer 
may  retain  the  old  price  list  and  offer  a  discount.  If  the  price 
varies,  the  dealer  may  vary  the  discount.  If  the  price  falls 
three  times  in  succession,  the  dealer  may  offer  three  different 
discounts. 


PERCENTAGE  161 

When  there  are  more  trade  discounts  than  one,  they  are 
called  a  discount  series. 

273.  Trade  discount  is  reckoned  as  a  per  cent  of  the  list 
price.     The  list  price  less  the  discount  is  the  Net  Price.     In  a 
discount  series,  the  first  discount  is  reckoned  on  the  list  price, 
and  each  subsequent  discount  is  reckoned  on  the  net  price — the 
price  after  deducting  the  preceding  discount. 

It  makes  no  difference  in  what  order  the  discounts  of  a 
series  are  considered.  A  series  of  20%,  15%,  and  10%  is  the 
same  as  10%,  20%,  and  15%.  But  20%,  15%,  and  15%  is 
not  the  same  as  20%  and  30%. 

274.  Discounts  are  usually  aliquot  parts  of  100,  and  opera- 
tions should  be  performed  with  aliquot  parts  when  practicable. 


MENTAL  PROBLEMS 

1.  Find  the  net  price  if  the  list  price  is  $12  and  the  trade 
discount  is  $25%. 

2.  Find  the  net  cost  of  10  boxes  of  soap  at  $4  per  box,  less 
12^-%  discount. 

3.  If  on  a  sale  of  $60  worth  of  goods  a  discount  of  15%  is 
allowed,  what  is  the  amount  of  discount?    What  is  the  net  cost? 

4.  A  dealer  sold  goods  listed  at  $80,  less  25%,  20%,  12£%. 
What  was  the  net  price  after  the  first  discount?     After  the 
second?     After  the  third? 

5.  Find  the  net  selling  price  of  an  article  marked  $6,  less  a 
discount  of  15%. 

6.  What  is  the  cost  of  25  yd.  of  cloth  at  $2,  less  discounts 
of  20%  and  10%? 

7.  What  is  the  cost  of  goods  listed  at  $75  and  sold  at  dis- 
counts of  20%,  25%,  33 J%,  and  50%? 

8.  What  will  a  $5  book  cost  if  discounted  at  15%? 

9.  Find  the  cost  of  goods  listed  at  $20,  less  30%  and  10%. 
10.  What  is  the  cost  of  20  cases  of  glass  at  $27,  less  dis- 
counts of  33£%  and  12|%? 


162  MODERN    COMMERCIAL   ARITHMETIC 

11.  Find  the   single   discount   equivalent  to  the  discount 
series  of  20%,  5%,  and  25%. 

SOLUTION.— The  net  price  after  the  first  discount  is  80%  of  the  list 
price.  After  the  second  discount  the  net  price  is  76 %  of  the  list  price. 
After  the  third  discount  the  net  price  is  57%  of  the  list  price.  If  the 
net  price  is  57%  of  the  list  price,  the  discounts  must  be  equivalent  to 
100%  —57%,  or  43%. 

Find  the  single  discount  equivalent  to  the  following  series: 

12.  10%,  10%.  22.  50%,  10   %,  20  %. 

13.  10%,  20%.  23.   25%,  20  %,  12£%. 

14.  15%,  20%.  24.  20%,    5  %,  25  %. 

15.  20%,    5%.  25.  12%,  50  %. 

16.  5%,  10%,  20  %.  26.   10%,  33£%,  20  %. 
X  17.  10%,  10%,  10   %.  27.  10%,  16|%. 

18.  20%,  20%,  20  %.  28.  24%,  25   %. 

IP.  20%,  10%,  121%.  29.  35%,  20   %. 

V   20.     6%,  10%.  50.   13%,  33*%. 

21.  25%,  10%.  31.  12%,  25  %,  331%. 

32.  What  must  I  ask  for  an  article  so  that  I  may  allow  a 
discount  of  20%  and  still  receive  $40  for  it? 

NOTE. — The  net  price  is  what  per  cent  of  the  asked  price? 

83.  Cloth  costing  $4  per  yard  must  be  marked  at  what  price 
to  gain  25%  and  allow  a  discount  of  20%? 

34*  At  what  price  must  I  mark  goods  costing  $18,  that  I 
may  allow  a  discount  of  25%  and  sell  them  at  a  gain  of  331%? 


PROBLEMS 

1.  What  is  the  net  cost  of  a  bill  of  goods  amounting  to 
discounted  at  30%  and  18%? 

NOTE.— Each  discount  may  be  taken  out  separately,  or  one  equiv- 
alent discount  may  be  used. 

2.  Find  the  net  cost  of  a  bill  of  goods  invoiced  at  $825  and 
discounted  at  25%,  20%,  10%. 


PERCENTAGE  163 

3.  Three  houses  list  similar  goods  at  $1260.  One  offers  dis- 
counts of  25%  and  25%  ;  another  offers  20%,  20%,  and  10%  ; 
and  the  third  offers  35%  and  15%.  What  is  the  net  price  of 
each  house? 

V'  4.  I  bought  goods  at  30%  and  20%  from  the  list  price  of 
$1475,  and  sold  them  at  20%,  10%,  and  20%  from  the  list 
price.  How  much  did  I  gain? 

5.  A  dealer  offers  bicycles  at  $100,  subject  to  discounts  of 
40%,  20%,  and  15%.     How  much  will  1  doz.  bicycles  cost? 

6.  A  book  costs  $5.     What  must  be  the  marked  price  to 
gain  20%,  and  allow  discounts  of  20%  and  25%? 

REMARK. — The  book  must  be  sold  for  $5  plus  20 %  of  $5,  or  $6.  A 
discount  of  20%  and  25%  is  equivalent  to  a  discount  of  40%.  If  40% 
discount  is  allowed,  then  $6  is  60%  of  the  marked  price. 

7.  Carpet  costing  $4  per  yard  must  be  marked  at  what  price 
/\to  gain  25%  and  allow  discounts  of  15%  and  20%? 

8.  Goods  listed  at  $265,  and  bought  at  discounts  of  28% 
and  12^%,  must  be  marked  at  what  price  to  gain  33-J-%  and 
allow  discounts  of  24%  and  16|%? 

9.  A  dealer  sells  goods   at  a   discount  of  25%   from  the 
marked  price  and  makes  a  profit  of  25%.     At  what  per  cent 
above  cost  did  he  mark  the  goods? 

10.  Find  the  cost: 

LIST  PRICE  DISCOUNT 

(a)  $  126.50  15  %,  12£% 

(V)  $  872.60  33£%,  25   % 

(c)  $  150.25  30   %,  20   %,    15   % 

(d)  $1285  40  %,  33 £%,  12|% 
(«)  $1673.80  15  %,  20  %,  16|% 
(/)  $4896.20  35  %,  22  %,   8  % 
(g)  $5325.75  24  %,  16  %,  12  % 
(4)  $  436.18  16f%,  12|% 

0)  $1120         30  %,  25  %,  15  % 
0')  $1736         45  %, 


164  MODERN"    COMMERCIAL    ARITHMETIC 

11.  At  what  per  cent  above  cost  must  goods  be  marked  to 
allow  a  discount  of: 

(a)  25   %  and  make  20  %  on  the  cost? 

(b)  10  %  and  make  25   %  on  the  cost? 

(c)  20   %  and  make  15   %  on  the  cost? 

(d)  10   %  and  make    8   %  on  the  cost? 

(e)  33£%  and  make  12|%  on  the  cost? 
(/)  40   %  and  make  25   %  on  the  cost? 
(g)  10   %  and  make  50   %  on  the  cost? 
(h)  .25   %  and  lose  15%  on  the  cost? 
(i)  50  %  and  neither  gain  nor  lose? 
(/)  15   %  and  lose  10%  on  the  cost? 

12.  Which  is  the  better   discount   offer,   25%,  20%,  and 
15%,  or  50%. 

MABKING   GOODS 

275.  Merchants  often  mark  the  cost  and  the  price  of  their 
goods  with  symbols  instead  of  figures.     Sometimes  the  selling 
price  is  in  figures  and  the  original  cost  in  symbols. 

276.  In  marking  by  symbols,  ten  letters  of  the  alphabet 
are  used  to  correspond  to  the  ten  figures  of  the  Arabic  notation. 
A  word  or  phrase  containing  ten  letters,  no  two  being  alike, 
is  taken  as  a  "key."     Some  words  and  phrases  used  as  keys 
are:  blacksmith,  handsomely,  what  prices,  cash  profit,  black 
horse.     The  value  of  each  letter  of  the  key  is  determined  by 
its  position  in  the  word  or  phrase.     Thus : 

blacksmith 
1234567890 

For  $1.25  write  Wc\  for  $2.68  write  lsi\  for  $4.77  write  cmm. 
Instead  of  repeating  a  letter,  as  in  cmm,  a  letter  not  found  in 
the  key  may  be  used  as  a  repeater.  Thus,  $4.77  might  be 
written  cmr9  using  r  to  show  that  m  is  repeated. 

The  last  two  letters  in  the  expression  represent  cents. 

If  a  period  is  added,  it  shows  that  there  are  no  cents.  Thus, 
Ilk.  means  $125. 


PERCENTAGE  165 

When  the  selling  price  is  given  in  figures,  and  the  cost  mark 
is  used,  the  selling  price  is  written  above  the  cost  mark.  Thus, 

'      means  that  the  selling  price  is  $1.50  and  the  cost  is  $1.25. 
ollc 

When  both  cost  and  selling  price  are  given,  two  keys  may 
be  used,  one  for  the  cost  and  the  other  for  the  selling  price. 
Thus,  using  "what  prices"  for  the  selling  price  and  "black- 

filj^")  Q 

smith"  for  the  cost  mark,  -=~-^  means  that  the  selling  price  is 

ollc 

$1.50  and  the  cost  is  $1.25. 


PROBLEMS 

1.  Write  the  following  prices,  using  "handsomely"  as  the 
key:    $1.25,  $2.25,  $4.17,  $1.87,  $2,65,  75^,  36^,  $1.95,  $3.33, 
$4.35. 

2.  Interpret  with  the  same  key:  liss,  smy,  II,  ahe,  nos,  das, 
eyy,  may,  hams. 

3.  Mark  all  of  the  above  prices  25%  advance,  using  the 
same  key. 

4.  With  the  same  key  for  the  cost  price  and  "what  prices" 
for  the  selling  price,  mark  the  following : 


COST 

GAIN 

COST 

GAIN 

(a)  $1.50 

25   % 

(/)    $2.00 

15  % 

(b)       .80 

20   % 

(3)     !-60 

25   % 

(c)     1.75 

33J% 

(Ji)       .90 

16|% 

(d)     2.40 

12*% 

(0      1.20 

75  °L 

(e)      1.25 

33J% 

0')     1-40 

30  % 

MENTAL  PROBLEMS 

Use  the  key  "blacksmith"  and  y  as  a  repeater.     Give  the 
cost  mark  for  the  following: 

1.  $1.45.  4.  $  .85.  7.  $7.50.  10.  $3.20. 

2.  2.25.  5.     1.60.  8.     8.25.  11.     6.85. 

3.  5.20.  6.       .90.  9.     2.15.  12.     1.75. 


166  MODERN   COMMERCIAL   ARITHMETIC 

STORAGE 

277.  Storage  is  the  price  or  amount  charged  for  storing 
goods  in  a  warehouse. 

Storage  is  usually  computed  by  the  weight,  measure,  or 
quantity  of  the  goods  stored.  Sometimes  it  is  computed  as  a 
per  cent  of  the  value  of  the  goods. 

278.  The  Term  of  Storage  is  the  time  for  which  the  charge 
is  made.     Storage  may  be  charged  by  the  day,  week,  or  month, 
and  a  fractional  part  of  a  term  is  counted  as  a  full  term. 

279.  Average  Storage. — When  the   quantity  of   goods  in 
storage  varies  on  account  of  additions  to  or  withdrawals  from 
the  stock,  charge  is  made  on  each  quantity  for  the  actual  num- 
ber of  days  it  is  stored,  and  an  average  term  of  storage  and  an 
average  quantity  stored  is  ascertained. 

EXAMPLE. — A  man  deposits  400  bu.  of  wheat,  and  after  20 
days  withdraws  100  bu. ;  the  rest  he  withdraws  in  15  days. 
What  is  the  storage  charge  at  1^  per  bushel  per  month? 

SOLUTION.— The  storage  of  400  bu.  for  20  days  is  equivalent  to  the 
storage  of  1  bu.  for  8000  ^days,  the  storage  of  300  bu.  for  15  days  is 
equivalent  to  the  storage  of  1  bu.  for  4500  days,  and  the  whole  storage 
is  equivalent  to  the  storage  of  1  bu.  for  12500  days.  The  average  time 
reduced  to  months  is  (12500 -f-  30  =  416f)  41?  months.  The  charge  for 
1  bu.  for  417  months  is  $4. 17 ;  therefore  the  charge  for  400  bu.  for  20 
days  and  300  bu.  for  15  days  is  14.17. 

280.  Sometimes  storage  is  paid  on  each  withdrawal  from 
the  warehouse.     This  is   Cash  Storage.     Sometimes  storage  is 
not  paid  until  the  last  withdrawal  is  made.     This  is  Credit 
Storage. 

PROBLEMS 

1.  (Simple  Storage.) — Find  the  storage  on  4500  bu.  of 
wheat  for  3  mo.  20  da.,  at  1$  per  bushel  per  month;  1735  bu. 
of  corn  for  4  mo.,  at  f^  per  bushel;  2863  bu.  of  oats  for  4  mo. 
15  da.,  at  £0  per  bushel;  1160  bbl.  of  flour  for  3  mo.  25  da., 
at  6^  per  barrel;  845  bu.  of  potatoes  for  1  mo.  18  da..,  at  10. 

NOTE.— Fractional  terms  count  as  whole  terms. 


PERCENTAGE  167 

2.  (Average  Cash  Storage.) — A  dealer  deposits  in  a  ware- 
house 460  bbl.  apples  Oct.  3 ;  632  bbl.  pears  Oct.  6 ;  535  bbl. 
potatoes  Oct.  15 ;  and  782  bbl.  apples  Oct.  25.  He  withdraws 
the  whole  on  Feb.  1.  What  are  the  storage  charges  at  4^  per 
barrel  per  month? 

OPERATION 

460  bbl.  for  121  da.  =  1  bbl.  for  55660  da. 
632  bbl.  for  ?  da.  =  1  bbl.  for  ?  da. 
535  bbl.  for  ?  da.  =  1  bbl.  for  ?  da. 
782  bbl.  for  ?  da.  =  1  bbl.  for  ?  da. 

Total  storage  =  1  bbl.  for      ?     da.  or  ?  mo. 


8.  Find  the  storage  charges,  at  1-J-^  per  bushel  per  month, 
on  the  following  deposits :  July  21,  8140  bu. ;  Aug.  1, 1670  bu. ; 
Aug.  15,  1985  bu.;  Sept.  1,  2430  bu.  All  was  withdrawn 
Dec.  20. 

4.  (Average  Credit  Storage.) — Find  the  storage  charges,  at 
3^  per  bbl.  per  month,  on  the  following : 

DEPOSITS  WITHDRAWALS 

Sept.    1,    810  bbl.  Sept.  12,  260  bbl. 

Sept.  15,  1460  bbl.  Sept.  25,  483  bbl. 

Oct.    24,   735  bbl.  Dec,      1,  the  remainder 


OPERATION 

810  bbl.  stored  for  11  da.  =  1  bbl.  for  ?  da. 
260  bbl.  withdrawn 


550  bbl.  stored  for    3  da.  =  1  bbl.  for  ?  da. 
1460  bbl.  deposited 

2010  bbl.  stored  for  10  da.  =  1  bbl.  for  ?  da. 

483  bbl.  withdrawn 
1527  bbl.  stored  for  29  da.  =  1  bbl.  for  ?  da. 

735  bbl.  deposited 

2262  bbl.  stored  for  38  da.  =  1  bbl.  for  ?  da. 
Total  storage  =  1  bbl.  for  ?  da. 


168  MODERN    COMMERCIAL   ARITHMETIC 

5.  The  deposits  and  withdrawals  of  goods  at  a  warehouse 
were  as  follows : 

DEPOSITS  WITHDRAWALS 

June    1,  240  bales  June  18,  160  bales 

June  28,  673  bales  July     3,  540  bales 

July  10,  490  bales  Aug.  15,  the  remainder 

Find  the  storage  bill  at  6^  per  bale  per  month. 

6.  Find  the  storage  bill  of  the  following,  at  3<p  per  case  per 
month: 

DEPOSITS  WITHDRAWALS 

Dec.    1,     431  cases  Dec.   28,  975  cases 

Dec.  23,     763  cases  Feb.      1,  648  cases 

Jan.  18,  1145  cases  March  4,   the  remainder 

7.  Find  the  storage  to  Dec.   1,  1902,  on  200  bbl.  apples 
deposited  Oct.  3,  1902,  at  3^  per  bbl.  per  mo. ;  350  bbl.  beans 
deposited  Oct.  1,  1902,  at  3^  per  bbl.  per  mo.;  5800  bu.  pota- 
toes deposited  Sept.  12,  1902,  at  1^  per  bu.  per  mo. 

8.  Find  the  storage  charges,  at  2^  per  bbl.  per  mo.,    due 
Dec.  15,  1902,  on  the  following  deposits:    Aug.  14,  1902,  450 
bbl.  vinegar;  Aug.  30,  1902,  425  bbl.  molasses;  Sept.  12,  1902, 
580  bbl.  sugar;  Sept.  18,  1902,  170  bbl.  pork. 

9.  Find  the  storage  of  the  following,  at  2^  per  bu.  per  mo. : 

DEPOSITS  WITHDRAWALS 

June  12,  140  boxes  June  19,    60  boxes 

June  27,  230  boxes  July  22,  210  boxes 

July  16,  175  boxes  Aug.  26,  the  remainder 

10.  Find  the  storage  of  the  following,  at  1^  per  bu.  per  mo. : 

DEPOSITS  WITHDRAWALS 

Aug.  12,  250  bu.  Sept.  10,  200  bu. 

Aug.  21,  380  bu.  Oct.    24,  150  bu. 

Sept.  25,  570  bu.  Nov.     3,  the  remainder 


INSURANCE 

281.  Certain  property  may  be  damaged,  or  destroyed  by 
fire,  water,  wind,  lightning,  etc.     Domestic  animals  die.     Per- 
sons may  be  afflicted  with  accidents  or  sickness,  and  all  must 
die.     A  sum  guaranteed  to  be  paid  in  case  of  any  such  misfor- 
tune is  called  Insurance. 

282.  The  Beneficiary  is  the  one  to  whom  the  insurance  is 
guaranteed  to  be  paid. 

283.  The  Insurance  Party  (Insurance  Company)  is  the 
party  that  agrees  to  pay  the  insurance. 

284.  The   Policy   is   the   written    contract    between  the 
insured  party  and  the  insurance  company. 

285.  The  Premium  is  the  amount  the  insured  party  agrees 
to  pay  the  insurance  company  for  the  insurance. 

286.  The  Term  of  Insurance  is  the  time  for  which  the 
policy  is  issued,  and  is  usually  one  or  more  years. 

287.  Insurance  Kates  are  given  as  a  certain  per  cent,  or  as 
so  much  per  $100  or  $1000  of  the  amount  of  insurance,  and 
depend  upon  the  risk  assumed  and  the  term  of  insurance. 

288.  An  Insurance  Agent  is  one  through  whom  the  insur- 
ance company  transacts  business  with  the  insured. 

289.  A  company  in  which  the  profits  and  losses  are  shared 
by  stockholders  is  a  Stock  Company. 

290.  A  company  in  which  the  profits  and  losses  are  shared 
by  the  parties  insured  is  a  Mutual  Insurance  Company. 

291.  The  two  general  kinds  of  insurance   are   Property 
Insurance  and  Personal  Insurance. 

PROPERTY    INSURANCE 

292.  Property  insurance  includes: 

Fire  Insurance — which  is  an  indemnity  for  loss  by   fire, 
water,  wind,  etc. 

Marine  Insurance — which  is  an  indemnity  for  loss  of  vessel 
or  cargo. 

169 


170  MODERN   COMMERCIAL  ARITHMETIC 

Live  Stock  Insurance — which  is  an  indemnity  for  loss  from 
death  of  domestic  animals. 

293.  In  an  Ordinary  Policy,  the  insurance  company  agrees 
to  pay  any  damage  that  does  not  exceed  the  face  of  the  policy. 
Thus,  if  a  house  worth  $10000  is  insured  for  $6000,  and  is  dam- 
aged  to   the   extent   of  $5000,  the  company  is  hound  to  pay 
$5000.     If  the  house  is  entirely  destroyed,  the  company  will 
pay  $6000. 

294.  In  an  Average  Clause  Policy,  the  insurance  company 
agrees  to  pay  such  a  part  of  the  loss  as  the  face  of  the  policy  is 
part  of  the  value  of  the  thing  insured.     Thus,  if  a  ship,  valued 
at  $10000,  is  insured  for  $6000,  and  is  damaged  to  the  extent 
of  $5000,  the  company  will  pay  only  $TVo°inr  or  £  of  $5000.     If 
the  whole  ship  is  destroyed,  the  company  will  pay  f  of  $10000. 

Marine  insurance   policies   usually   contain    the    "average 
clause." 

MENTAL  PROBLEMS 

1.  Find  the  cost  of  insuring  a  house  for  $2000  if  the  rate  of 
insurance  is  2£%. 

2.  What  is  the  premium  on  $700  of  insurance  at  3%? 

3.  Find  the  cost  of  $5800  insurance  at  $2  per  $100. 

4.  I  insured  my  house  for  $2500  for  3  yr.,  at  2%.     After 
6  mo.  the  policy  is  cancelled.     What  sum  should  the  company 
repay  me? 

5.  At  2%,  what  amount  of  insurance  can  I  obtain  for  $28? 

6.  A  ship  worth  $12000  is  insured  for  $6000  in  an  average 
clause  policy.     If  the  vessel  is  damaged  to  the  extent  of  $2500, 
what  sum  must  the  company  pay? 

7.  The  amount  insured  is  what  element  in  percentage? 

8.  The  premium  paid  is  what  element? 

9.  The  loss  sustained  is  what  element? 

10.  If  I  pay  $30  for  insuring  property  worth  $9000  and  the 
property  is  destroyed,  what  is  my  net  loss? 

11.  If  I  pay  $20  for  insuring  $5000  worth  of  property,  what 
is  the  rate  per  cent  of  premium? 

12.  What  is  the  premium  on  an  insurance  of  $1600,  for 
3  yr.,  at  l-J-%  per  annum? 


INSURANCE  171 

PROBLEMS 

1.  What  premium  must  be  paid  on  an  insurance  of  $2375 
at  lf%? 

2.  A  steamer,  worth  $260000,  was  insured  for  $180000,  at 
2^%,  in  a  policy  with  the  average  clause.     If  the  boat  was 
damaged  to  the  extent  of  $75000,  what  was  the  net  loss  to  the 
owners? 

3.  If  the  Commercial  Insurance  Company  insure  property 
for  $578000,   at  2£%,  and  reinsure  f  of  the  risk  in  another 
company  at  2f  %,  what  would  be  the  loss  to  the  Commercial 
Company  if  the  property  becomes  destroyed? 

4.  A  dealer  bought  1270  bbl.  of  flour  at  $5.30  per  barrel, 
and  had  it  insured  at  £ %.     If  80  bbl.  are  destroyed,  at  what 
price  per  barrel  must  he  sell  the  remainder  to  make  a  net  profit 
of  20%  on  the  money  invested? 

5.  What  is  the  premium  on  a  $4860  insurance  policy,  at 
37^  per  $100? 

6.  Find  the  premium  on  an  insurance  for  $135725,  at  $22.50 
per  $1000. 

7.  A  cargo  worth  $40000  was  insured  for  $25000,  in  a  policy 
with  the  average  clause,  at  $2.10  per  $100.     In  case  of  damage 
to  the  extent  of  $18000,  what  would  be  the  total  loss  to  the 
owner? 

8.  A  train  load  of  flour  of  1670  bbl.,  worth  $6.40  per  bbl., 
is  insured  for  two-thirds  of  its  value,  at  lf%.     If  the  flour  is 
destroyed,  how  much  will  the  owner  lose? 

9.  There   is   an  insurance  of    $85000  on   a  factory  worth 
$120000,  $25000  on  machinery  worth  $40000,  and  $18000  on 
material  worth  $24000.     The  building  is  entirely  destroyed,  the 
machinery  is  damaged  to  the  extent  of  $16000,  and  the  mate- 
rial is  damaged  to  the  extent  of  $1500.     If  the  rate  of  insur- 
ance is  If  %,  how  much  does  the  company  lose?     How  much 
would  the  owner  lose  if  the  policy  contained  an  average  clause? 

10.  Which  is  the  better  rate  of  insurance,  2J%  or  $22.50 
per  $1000? 

11.  At  2J%,  in  how  many  years  would  the  premium  paid 
equal  the  face  of  the  policy? 


172  MODERN    COMMERCIAL   ARITHMETIC 

12.  A  man  bought  a  house  for  $2340,  had  it  insured  for  f 
its  value,  at  75^  per  $100,  and  sold  it  for  $2560.  What  was  his 
gain  per  cent? 

18.  If  I  take  out  two  policies  for  $1900  and  $2100  on  a 
building,  how  should  a  damage  of  $1475  be  divided  between  the 
two  companies? 

PERSONAL  INSURANCE 

295.  Personal  insurance  includes : 

Life  Insurance — which  is  an  indemnity  for  loss  by  death. 

Accident  Insurance — which  is  an  indemnity  for  loss  by  acci- 
dent. 

Health  Insurance — which  is  an  indemnity  for  loss  by  sickness. 

Under  a  health  policy  the  insured  receives  a  certain  sum  per 
week  during  the  continuance  of  the  disability. 

Under  an  accident  policy  the  insured  receives  a  certain  sum 
for  the  loss  of  some  bodily  organ — as  an  eye  or  hand — and  a 
weekly  indemnity  for  a  temporary  disability. 

296.  The  two  chief   kinds  of   life  insurance  policies  are 
the  Life  Option  Policy  and  the  Endowment  Policy. 

The  policies  of  the  different  companies  differ  in  some 
respects,  but  the  policies  of  all  first-class  companies  are  very 
much  alike,  all  being  based  on  recognized  business  principles. 

297.  There  are  two  kinds  of  life  option  policies — the  ordi- 
nary life  policy  and  the  term  payment  life  policy.     Every  pol- 
icy is  a  contract.    Under  the  ordinary  policy  the  person  insured 
agrees  to  pay  the  company  certain  premiums  annually  as  long 
as  he  lives;  and  the  insurance  company  agrees  to  pay,  upon  the 
death  of  the  insured,  a  certain  sum  called  the  face  of  the  pol- 
icy, to  the  person  mentioned  in  the  policy  as  the  beneficiary. 
If  the  insured  dies  after  the  first  payment,  the  beneficiary  gets 
the  full  face  of  the  policy — usually  one  or  more  thousand  dol- 
lars.    If  he  pays  premiums  for  fifty  years,  and  then  dies,  the 
beneficiary  gets  the  face  of  the  policy,  and  under  some  policies 
he  may  also  receive  an  additional  payment,  known  as  "accumu- 
lated dividends."     Such  a  policy  is  called  a  " participating  pol- 
icy, "  because  the  policy  holder  participates  in  the  division  of 


INSURANCE  173 

certain  profits  of  the  company.  A  policy  under  which  the 
beneficiary  receives  only  the  face  of  the  policy  is  called  a  " non- 
participating"  policy.  The  premium  on  a  participating  policy 
is  greater  than  on  a  non-participating  policy.  On  a  $1000 
participating  life  option  policy  of  the  National  Life  Insurance 
Company,  a  person  insured  at  the  age  of  20  years  would  pay  an 
annual  payment  of  $18.73.  At  his  death  his  beneficiary  would 
receive  $1000  plus  the  accumulated  dividends.  On  a  non- 
participating  policy  the  premium  would  be  $15. 57.  If  the  person 
insured  is  40  years  old,  he  would  have  to  pay  on  a  non-partici- 
pating policy  for  $1000  an  annual  premium  of  $26.75.  Of  course, 
a  person  40  years  old  is  likely  to  die  twenty  years  sooner  than 
one  20  years  old,  and  if  the  same  sum  is  to  be  paid  at  the  death 
of  each,  the  older  ought  to  pay  more  per  annum  while  he 
lives.  If  he  were  60  years  old  the  premium  would  be  $62.97. 

We  may  ask,  how  does  the  insurance  company  get  the  $1000 
to  pay  in  the  case  of  a  man  who  puts  in  $15.57  and  then  dies? 
How  does  the  company  make  anything  by  that?  A  person  at 
the  age  of  20  years  takes  a  policy  for  $1000,  pays  in  $15.57  for 
fifty  years  and  dies.  If  he  had  put  his  payments  in  a  bank,  at 
3%  interest,  they  would  have  amounted,  at  his  death,  to 
$1808.92,  and  at  4%  they  would  have  amounted  to  $2472.05. 
The  company  pays  only  $1000.  Those  who  insure  at  20  years 
die  at  different  ages,  and,  on  the  average,  the  insurance  com- 
pany can  pay  the  policy  and  still  make  money. 

As  a  business  venture,  does  it  pay  to  insure?  If  I  die  early, 
yes.  If  I  live  as  long  as  the  average  person  or  longer,  no.  So 
the  question,  "Will  it  pay  me  to  insure?"  is  simply,  "How 
long  will  I  live?"  and  no  one  can  tell. 

But  there  is  another  side.  Suppose  a  young  man  has  a 
wife,  children,  or  parents  dependent  upon  his  labor  for  support. 
If  he  lives  he  can  support  them,  but  if  he  dies  early  their  means 
of  support  is  gone.  If  he  has  his  life  insured,  he  leaves 
something  for  their  support.  If  he  insures,  he  runs  the  risk 
of  paying  in  more  than  he  draws  out.  If  he  does  not  insure, 
he  runs  the  risk  of  dying  soon,  and  not  leaving  behind  an 
adequate  sum  for  the  support  of  those  dependent  upon  him. 


174  MODERN    COMMERCIAL   ARITHMETIC 

Under  a  term  life  policy  the  insured  pays  10,  15,  or  20 
annual  premiums,  and  then  his  insurance  matures,  Jiis  policy 
becomes  paid  up,  and  he  has  no  more  premiums  to  pay.  Of 
course,  the  rates  for  a  term  policy  are  higher  than  for  a  life 
policy.  The  annual  premium  on  a  twenty-payment  non-par- 
ticipating life  policy  (one  that  becomes  paid  up  after  twenty 
annual  premiums  have  been  paid)  is  $25  for  a  person  20  years 
of  age,  and  $35.82  for  a  person  40  years  of  age. 

398.  An  Endowment  Policy  is  one  in  which  the  face  of 
the  policy  is  payable  at  death  or  a  certain  number  of  years 
after  date,  even  if  the  person  insured  is  alive  at  that  time. 
Thus,  if  a  man  20  years  of  age  takes  a  twenty-year  endowment 
policy  for  $1000,  and  dies  the  next  year,  or  any  time  within 
twenty  years,  his  beneficiary  receives  $1000.  If  the  man  lives 
twenty  years,  the  beneficiary  receives  $1000  at  the  end  of  that 
time,  and  the  beneficiary  may  be  the  person  insured.  The 
premium  on  an  endowment  policy  is  higher  than  on  a  life 
policy.  The  premium  on  a  twenty-year  non-participating 
endowment  policy  for  $1000  on  the  life  of  a  person  20  years  of 
age  is  $44.07  in  the  National  Life  Insurance  Company. 

If  a  person  20  years  of  age  takes  a  straight  life  policy  for 
$1000,  he  pays  $15.57  per  year  till  death.  If  he  takes  a 
twenty-year  payment  life  policy,  he  pays  $25  for  twenty  years 
only.  If  he  takes  a  twenty-year  endowment  policy,  he  pays 
$44.07  for  twenty  years  only.  In  any  case,  $1000  would  be 
payable  at  his  death.  In  the  last  case,  $1000  would  be  pay- 
able at  the  end  of  twenty  years,  even  if  the  person  insured  lives. 
If  a  person  should  die  soon  after  he  is  insured,  the  straight  life 
policy  is  the  best,  but  if  he  is  going  to  live  forty  or  fifty  years, 
the  endowment  policy  is  the  best.  So  again  the  question  is, 
"How  long  shall  I  live?" 

299.  Cash  Surrender  Value. — Usually,  after  three  or  more 
annual  premiums  have  been  paid,  a  policy  may  be  surrendered 
to  the  company,  which  will  pay  the  person  insured  a  certain 
sum,  the  cash  surrender  value  of  the  policy. 

300.  Paid-up  Insurance. — After    three   or    more  annual 
premiums  have  been  paid,  the  insured  may  surrender  his  policy 


INSURANCE 


175 


and  receive  a  policy  for  a  lesser  amount,  but  he  will  not  have 
to  pay  any  more  premiums. 

301.  Extended  Insurance. — After  making  three  or  more 
annual  payments,  he  may  stop  paying,  keep  his  policy,  and 
have  his  insurance    extended  for  a  certain  number  of  years. 
Thus,  if  a  man  40  years  of  age  takes  a  twenty-payment  life 
policy,  makes  ten  annual  payments  and  stops,  he  may  be  insured 
for  15  yr.  288  da.  longer  without  the  further  payment  of  any 
premiums,  but  at  the  end  of  that  time  his  policy  expires. 

302.  The  annual  premium  on  the  non-participating  life 
option,  twenty-payment  life,  and  twenty-year  endowment  poli- 
cies, for  $1000,  as  given  by  one  of  the  standard  life  insurance 
companies,  is  shown  by  the  following : 

TABLE    OF    KATES 


PREMIUM 

AGE 

LIFE 

20-PAYMENT 

LIFE 

20-  YEAR 
ENDOWMENT 

20  

$15.57 

$25.00 

$44.07 

21  

15.91 

25.37 

44.11 

22  

16.26 

25.76 

44.16 

23  

16.63 

26.16 

44.21 

24  

17.01 

26.57 

44.26 

25  

17.42 

27.00 

44.32 

26  

17.84 

27.44 

44.39 

27  

18.29 

27.90 

44.46 

28  

18.75 

28.38 

44.53 

29  

19.24 

28.87 

44.62 

30  

19.76 

29.38 

44.71 

31  

20.30 

29.91 

44.82 

32  

20.88 

30.47 

44.93 

33  

21.48 

31.04 

45.06 

34  

22.11 

31.64 

45.20 

35  

22  78 

32  26 

45.36 

36  

23.49 

32.91 

45.53 

37.   ... 

24  24 

33  59 

45  73 

38  

25  03 

34  30 

45.96 

39  

25  87 

35  04 

46.21 

40  

26.75 

35.82 

46.4S 

176  MODERN   COMMERCIAL   ARITHMETIC 

PROBLEMS 

1.  A  man  at  the  age  of  25  took  a  $3000  twenty-payment 
life  policy.     He  died  after  paying  10  premiums.     What  was  the 
annual  premium?     How  much   did  his  family  receive  at  his 
death?     How  much  would  the  premiums  paid  have  amounted 
to  at  the  time  of  his  death,  if  they  had  been  deposited  in  a 
bank  at  3|%  compound  interest? 

SOLUTION.— $27  X  3  =  $81,  premium.     See  table,  page  175. 
$12.14  X  27  =  $327.78,  amount  of  10  premiums  of  $27  at  %\% .     See 
table,  page  194. 

2.  A  man  36  years  old  takes  out  an  endowment  policy  for 
$2000.     What  annual  premium  must  he  pay?     If  he  lives  20 
years  and  receives  the  $2000  insurance,  how  much  less  will  he 
receive  than  he  would  have  received  if  he  had  invested  his 
premiums  at  4%  compound  interest? 

3.  A  man  21  years  old  takes  a  twenty- payment  life  policy 
for  $2000,  and  dies  at  the  age  of  45.     How  much  will  his  fam- 
ily receive  from  the  insurance  company?     How  much  would 
they  have  received  if  he  had  deposited  the  premiums  in  a  bank 
at  3^%  compound  interest? 

4.  3  men,  each  aged  26,  take  out  policies  for  $3000  each; 
one  takes  a  life  option  policy,  one  a  twenty-payment  life  policy, 
and  the  third  a  twenty-year  endowment  policy.     They  all  die 
at  the  age  of  37.     Show  what  the  premiums  paid  by  each  would 
have  amounted  to  at  4%  compound  interest. 

5.  Suppose  the  men  mentioned  in  the  last  example  had  died 
at  the  age  of  57.     Show  what  the  payments  in  premiums  of  the 
first  man  would  have  amounted  to  at  4%  compound  interest, 
and  what  his  family  received.     Show  the  same  of  the  second 
man.       Show   the   same   of    the  third    man,    estimating   the 
amount  his  family  received  by  finding  the  amount  of  the  $3000 
endowment  at  4%  compound  interest  from  the  time  it  was  paid, 
to  the  time  of  his  death. 


INTEKEST 

SIMPLE  INTEREST 

303.  If  a  man  hires  a  horse,  he  pays  for  the  use  of  it.     If 

he  loans  a  sum  of  money,  he  asks  pay  for  its  use.  By  using 
money  in  business,  a  person  may  make  money.  Two  men  in 
partnership  may  run  a  store,  one  furnishing  the  labor  and  the 
other  the  money.  If  they  divide  the  profits  equally,  the  use  of 
the  money  of  the  one  is  considered  equivalent  to  the  labor  per- 
formed by  the  other.  If  A  owes  B  $100  and  does  not  pay  it  at 
once,  A  is  using  B's  money  and  should  pay  for  the  use  of  it. 

304.  Strictly  speaking,  Interest  is  the  use  of  money. 
The  common  acceptation  of  the  term  interest  is  the  money 

that  is  paid  for  the  use  of  money. 

305.  The  sum  for  whose  use  interest  is  paid  is  the  Prin- 
cipal. 

306.  The  sum  of  the  principal  and  interest  is  the  Amount. 
It  is  the  total  sum  the  debtor  owes  or  will  owe  at  the  maturity 
of  the  debt. 

307.  The  time  during  which  the  principal  is  used  is  the 
Term  of  Interest  or  the  Time. 

308*  Interest  is  computed  as  a  per  cent  of  the  principal. 

309.  The  Eate  of  Interest  is  the  rate  per  cent  charged  for 
the  use  of  the  principal.     If  the  rate  is  6%  per  annum,  the 
interest  for  one  year  is  6%  of  the  principal,  or  6^  on  $1. 

The  rate  of  interest  is  per  annum,  unless  otherwise  speci- 
fied. 

310.  The  law  of  most  States  fixes  a  limit  to  the  rate  of 
interest  that  may  be  charged.     This  is  called  the  maximum 

177 


178  MODERN    COMMERCIAL   ARITHMETIC 

rate.  Any  rate  of  interest  that  does  not  exceed  that  limit  is 
allowed.  It  also  fixes  a  rate  to  be  allowed  in  case  no  rate  is 
mentioned.  This  rate  is  called  the  Legal  Rate.  Usury  is 
interest  in  excess  of  the  maximum  rate. 

311.  The  interest  on  any  principal  for  any  given  time  is  a 
certain  per  cent  of  the  principal.     This  per  cent  is  the  rate 
of  interest  as  affected  by  the  term  of  interest.     If  the  rate  is 
6%  and  the    term  is  1  yr.,  the  interest  will  be  6%   of  the 
principal.     If  the  time  is  2  yr.,  the  interest  will  be  12%  of  the 
principal.     If  the  term  is  4  mo.,  the  interest  will  be  £  of  6%, 
or  2%  of  the  principal. 

312.  The  chief  problem  in  interest  is  to  take  the  rate  and 
term  into  consideration  and  find  what  per  cent  the  interest  is  . 
of  the  principal.  Months  are  twelfths  of  a  year.     Thirty  days 
are  considered  an  interest  month. 

313.  Interest  is  commonly  computed  on  a  basis  of  360  days 
for  a  year.     Interest  on  this  basis  is  called  Common  Interest. 
360  days  is  taken  as  a  year  for  convenience  in  computing  inter- 
est, and  it  is  sufficiently  exact  for  ordinary  business. 

314.  Exact  Interest  is  interest  for  the  exact  time  in  days 
considered  as  365ths  of  a  year. 

315.  Since  common  interest  is  based  on  a  360-day  year, 
the  common  interest  year  is  5  da. ,  or  T^-  of  a  year  shorter  than 
the  exact  year,  and  the  interest  for  a  given  number  of  days  by 
the  common  method  is  -fa  greater  than  the  interest  by  the  exact 
method.     Therefore,  to  find  exact  interest,  find  the  common 
interest  and  subtract  from  it  T^  of  itself. 

NOTE. — Exact  interest  is  taken  by  the  United  States  government 
by  some  banks  and  in  Ganada. 

316.  There  are  several    methods  of    computing  interest. 
Following  are  given  some  of  the  methods  that  are  among  the 
best.     The  pupil  may  familiarize  himself  with  all  and  select 
one  or  more  for  his  own  use. 


INTEREST  179 

Cancellation  Method 

317.  EXAMPLE.  —  Find  the  interest  on  $120  for  39  da. 
at  4%. 

OPERATION  EXPLANATION.—  39  da.  =  f/Q  yr.    The 

x  .04  x  30-^  interest  for  1  yr.  is  4%  of  $120,  therefore 

=  $-52.      the  interest  for  <£&  yr.  is  £&  of  .04  of 


?  $120.     The  product  of  the  principal,  rate, 

and  time  in  days  divided  by  360  equals 
the  interest.     We  have  this  formula: 
$?  X  t%  X  ?  da. 


360 


-  =  Interest. 


NOTES.— 1.  The  rate  per  cent  should  be  expressed  decimally. 
2.  Divide  when  you  can,  multiply  when  you  must. 


PROBLEMS 

Find  the  common  interest  on : 

1.  $840,  for  3  mo.  12  da.,  at  4%. 

2.  $126,  for  93  da.,  at  7%. 

S.  $278.50,  for  115  da.,  at  6%. 

4.  $396,  for  4  mo.,  at  8%. 

5.  $172.50,  for  63  da.,  at  5%. 

6.  $264.25,  for  27  da.,  at  6%. 

7.  $420,  for  18  da.,  at  3%. 

8.  $580.60,  for  7  mo.  8  da.,  at  4%. 

9.  $371,  for  9  mo.,  at  5%. 

10.  $218,  for  1  yr.  4  mo.,  at  6%. 

11.  $1130,  for  3  yr.  7  mo.,  at  4%. 

12.  $93,  for  1  yr.  3  mo.  12  da.,  at  6%. 
IS.  $1640.20,  for  84  da.,  at  4£%. 

14.  $793.80,  for  1  yr.  16  da.,  at  9%. 

15.  $784.30,  for  7  mo.  19  da.,  at  6%. 

16.  $2630,  for  2  yr.  12  da.,  at  5%. 

17.  $364,  for  8  mo.  15  da.,  at  8%. 

18.  $236.40,  for  2  yr.  4  mo.  15  da.,  at  6%0 
Find  the  exact  interest  on : 

19.  $375,  for  21  da.,  at  6%. 

20.  $421,  for  1  mo.  12  da.,  at  5%. 


180  MODERN    COMMERCIAL    ARITHMETIC 

21.  $1580.45,  for  2  yr.  3  mo.  15  da.,  at  4%. 

22.  $436,  for  7  mo.  15  da.,  at  6%. 
28.  $109.75,  for  9  mo.  11  da.,  at  5%. 

24.  $255,  for  4  mo.  12  da.,  at  3%. 

25.  $218.30,  for  1  yr.  11  mo.,  at  9%. 
Find  the  ordinary  interest  on : 

26.  $375.80,  for  19  da.,  at  7%. 

27.  $511.25,  for  2  yr.  6  mo.  9  da.,  at  4|%. 

28.  $928,  for  1  yr.  9  mo.  18  da.,  at  4%. 

29.  $1362.50,  for  1  yr.  11  mo.  15  da.,  at  6%. 

80.  $169.25,  for  10  mo.  21  da.,  at  5%. 

81.  $235.28,  for  3  mo.  16  da.,  at  3|%. 
32.  $417,  for  1  yr.  7  mo.,  at  4%. 

88.  $95.60,  for  2  yr.  3  mo.,  at  6%. 
84.  $125,  for  17  da.,  at  6%. 

35.  $962.75,  for  1  yr.  1  mo.  12  da.,  at  5%. 
86.  $65.20,  for  6  mo.  22  da.,  at  6%. 

37.  $144.10,  for  9  mo.  24  da.,  at  4%. 

38.  $216,  for  1  yr.  4  mo.,  at  3|%. 

89.  $96.50,  for  3  yr.  5  mo.  8  da.,  at  5%. 
40.  $1275, .for  4  yr.  10  mo.  20  da.,  at  6%0 

1000-Day  Method 

318.  Find,  by  the  cancellation  method,  the  interest  on  any 
sum  for  1000  da.,  at  36%. 

Principles. — 1.  For  the  interest  on  any  principal  for  1000 
da.  at  36%,  take  the  principal. 

2.  For  the  interest  on  any  principal  for  1  da.  at  36%,  point 
off  3  places  in  the  principal. 

3.  For  the  interest  on  any  principal  for  any  number  of  days 
at  36%,  multiply  the  principal  by  the  number  of  days  and 
point  off  3  places. 

OB, 

$?  x  36%  x  da.      _   ,  .  _ .   . 

—  =  Interest  at  36%. 


360 

Cancel  by  dividing  360  by  .36,  and 
$?xda. 


1000 


=  Interest  at  36%. 


INTEREST  181 

MENTAL  PROBLEMS 

Find  the  interest,  at  36%,  on: 

1.  $500,  for  22  da.  6.  $47,  for  12  da. 

2.  $480,  for  20  da.  7.  $70,  for  106  da. 

3.  $75,  for  2  mo.  8.  $83,  for  1  mo. 

4.  $130,  for  18  da.  9.  $90,  for  33  da. 

5.  $125,  for  3  mo.  10.  $1000,  for  62  da. 

11.  What  part  of  the  interest  at  36%  is  the  interest  at  6%? 
At  4%?     At  3%?     At  9%?     At  12%?     At  4|%?     At  2%? 
At5%?     At7%? 

12.  After  finding  the  interest  at  36%,  how  can  you  find  the 
interest  at  6%?     At  4%?     At  3%?     At  9%?     At  4|%?     At 
12%?     At5%? 

18.  Find  the  interest  on  $300,  for  80  da.,  at  6%. 

14.  Find  the  interest  on  $200,  for  75  da.,  at  9%. 

15.  Find  the  interest  on  $120,  for  18  da.,  at  4%. 

16.  Find  the  interest  on  $72,  for  40  da.,  at  8%. 

PROBLEMS 

Find  the  interest,  by  the  1000-day  method,  on: 

1.  $162.40,  for  81  da.,  at  4%.     11.  $235,  for  6  wk.,  at  9%. 

2.  $216,  for  17  da.,  at  6%.         12.  $742,  for  80  da.,  at  5%. 
S.  $328,  for  19  da.,  at  4£%.       18.  $315,  for  4  mo.,  at  3%. 

4.  $1114,  for  41  da.,  at  12%.  14.  $275,  for  2  wk.,  at  7%. 

5.  $265,  for  72  da.,  at  9%.  15.  $316,  for  33  da.,  at  6%. 

6.  $439.80,  for  69  da.,  at  3%.  16.  $529,  for  25  da.,  at  5%. 

7.  $276.25,  for  140  da.,  at  5%.  17.  $236,  for  40  da.,  at  4%. 

8.  $792,  for  63  da.,  at  7%.  18.  $427,  for  35  da.,  at  8%. 

9.  $168.25,  for  90  da.,  at  2%.  19.  $638,  for  21  da.,  at  6%. 
10.  $93.80,  for  2  mo.,  at  6%.  20.  $192,  for  15  da.,  at  5£%. 

Find  the  amount  of 

21.  $1420,  for  21  da.,  at  4%.  26.  $820,  for  2  mo.,  at  7%. 

22.  $975,  for  160  da.,  at  6%.  27.  $416,  for  93  da.,  at  3%. 
28.  $268,  for  5  mo.,  at  9%.  28.  $617,  for  33  da.,  at  2%. 

24.  $315,  for  6  wk.,  at  8%.          29.  $283,  for  45  da.,  at  4|%. 

25.  $276,  for  82  da.,  at  5%.         SO.  $116,  for  13  da.,  at  6% 


182  MODERN    COMMERCIAL   ARITHMETIC 

3.L  $728,  for  1  yr.  4  mo.  6  da.,  at  6%. 

82.  $520,  for  2  yr.  7  mo.  15  da.,  at  4%. 

38.  $1724,  for  1  yr.  8  mo.  20  da.,  at 

84.  $65,  for  11  mo.  27  da.,  at  5%. 

85.  $13850,  for  1  yr.  6  mo.  9  da.,  at 

86.  $768,  for  2  yr.  5  mo.  24  da.,  at  4%. 

87.  $195,  for  1  yr.  1  mo.  5  da.,  at  6%. 
38.  $252,  for  9  mo.  6  da.,  at  4%. 

89.  $332,  for  1  yr.  2  mo.,  at  7%. 

40.  $518,  for  3  yr.  9  mo.  11  da.,  at  8%. 

Banker's  60-Day  Six  Per  Cent  Method 

319.  The  most  common  rate  of  interest  is  6%. 

A  month  is  usually  considered  30  da.,  and  a  year  360  da. 
Most  notes  run  for  90  da.  or  less. 

320.  At  6%  per  annum,  the  interest  on  any  principal  for 
2  mo.  (60  da.,  J-  yr.)  is  1%  of  the  principal. 

321.  Principle. — To  find  1%  of  any  principal,  point  off  2 
places.     Therefore,  to  find  the  interest  on  any  sum  for  60  da.  at 
6  % ,  point  off  2  places. 

MENTAL  PROBLEMS 

1.  What  is  the  interest,  at  6%,  for  60  da.,  on  $46?    $57.30? 
$294?   $387?   $65.90?   $789?    $5076?   $54.90?  $3676?   $68.85? 
$2167? 

2.  30  is  what  part  of  60?     After  finding  the  interest  for 
60  da.,  how  can  you  find  the  interest  for  30  da.? 

8.  What  is  the  interest,  for  30  da.,  at  6%,  on  $240?    $560? 
$862?    $45.80?    $5680?    $34.25?    $67.90?    $346?    $80?    $740? 

4.  6  is  what  part  of  60?     After  finding  the  interest  for 
60  da.,  how  can  you  find  the  interest  for  6  da.?     How  many 
places  must  you  point  off  to  find  the  interest  on  any  sum,  at 
6%,  for  6  da.? 

5.  What  is  the  interest,  for  6  da.,  at  6%,  on  $580?    $720? 
$342?  $560?  $96.80?  $5678?  $89.56?    $52167?    $9076?    $3467? 
$43809? 


INTEREST 


183 


6.  After  finding  the  interest  for  6  da.,  how  can  you  find 
the  interest  for  3  da.? 

7.  20  is  what  part  of  60? 


322,  EXAMPLE  1.- 
at  6%. 

$  7 


-Find  the  interest  on  $720,  for  99  da., 


OPERATION 

20  =  int.  for  60  da. 
60  =  int.  for  30  da. 


72  =  int.  for 
36  =  int.  for 


6  da. 
3  da. 


$11   88  =  int.  for  99  da. 

EXAMPLE  2. — Find  the  interest  on  $480,  for  85  da.,  at  6%. 
OPERATION 

80  =  int.  for  60  da. 
60  =  int.  for  20  da. 
40  =  int.  for  5  da.  (j  of  20) 


$6  80  =  int.  for  85  da. 

NOTES.— 1.  To  find  the  interest  for  60  da.,  at  §%,  cut  off  2  places 
by  a  vertical  line.  For  4  mo.,  double  this,  for  6  mo.,  multiply  it  by 
3,  etc.  For  30  da.,  take  J  of  it;  for  20  da.,  take  J  of  it.  For  40  da., 
double  the  interest  for  20  da.  For  5  da.,  take  \  the  interest  for  20  da. 
For  6  da.,  cut  off  3  figures.  For  3  da.,  take  J  of  the  interest  for  6  da., 
for  2  da.,  take  J,  etc. 

2.  To  find  the  interest,  at  6% ,  for  any  time,  find  the  interest  for  60 
da.  Divide  the  given  number  of  days  into  aliquot  parts  of  60  da. ; 
and  compute  the  interest  on  each  number  of  days. 

EXAMPLE  3. — Find  the  interest  on  $980,  for  5  mo.  27  da., 
at  6%. 

OPERATION 

$  9   80  =  int.  for  60  da.  (2  mo.) 
19   60  =  int.  for    4  mo. 
4  90  =  int.  for    1  mo. 
3  27  =  int.  for  20  da. 
98  =  int.  for    6  da. 
16  =  int.  for    1  da. 


$28  91  =  int.  for    5  mo.  27  da. 


184 


MODERN    COMMERCIAL   ARITHMETIC 


323.  Following  are  given  some  groups  of  days  with  which 
the  pupil  should  be  familiar. 
Aliquot  parts  of  60  days  : 


15  = 


20  =  4 
Aliquot  parts  of  6  days: 


324.  Any  term  of  days  may  be  divided  into  convenient 
aliquot  parts,  as  shown  by  the  following  list,  which  should  be 
carefully  studied: 


5 

7 
8 
9 


3  +  2 
6  +  1 
6  +  2 
6  +  3 


11  =  10  +  1 
13  =  12  +  1 

16  =  10  +  6 

17  =  10  +  6  +  1 
18=    6x3 


21=    6x    3  +  3 

24  =    6  x    4,  12  x  2 

25  =  15  +  10 

26  =  20+    6 

27  =  15  +  12 

28  =  20+    6  +  2 

29  =  20+    6  +  3 
31  =  30+    1 
34=30+    2  +  2 


35  =  30+    3  +  2 

36  =  30+    6 

38  =  30+    6  +  2 

39  =  30+    6  +  3 
4?  =  30 +  12 

45  =  15  x    3 

46  =  20  x    2  +  6 

48=    6x    8,30  +  15  +  3 
97  =  60  +  30  +  6+    1 


PROBLEMS 


Find  the  interest,  at  6%,  on: 

1.  $480,  for  25  da.  11. 

2.  $1240,  for  29  da.  12. 

3.  $194,  for  58  da.  18. 

4.  $715,  for  87  da.  U. 

5.  $1213,  for  112  da. 

6.  $270.80,  for  6  mo.  11  da.  15. 

7.  $2045.60,  for  9  mo.  16  da.  16. 

8.  $697.25,  for  1  yr.  4  mo.  17. 

19  da.  18. 

9.  $833.50,  for  2  yr.  11  mo.  19. 

4  da.  20. 

10.  $573,  for  8  mo.  28  da.  21. 


$642,  for  7  mo.  17  da. 
$217.90,  for  5  mo.  21  da. 
$1063,  for  1  mo.  9  da. 
$2135,    for   1   yr.    4  mo. 

12  da. 

$652,  for  165  da. 
$79.86,  for  218  da. 
$473.95,  for  131  da. 
$238.70,  for  147  da. 
$3084,  for  1  yr.  3  mo. 
$541,  for  2  yr.  14  da. 
$148,  for  28  da. 


INTEREST  185 

22.  $375,  for  42  da.  82.  $194,  for  1  mo.  16  da. 

23.  $1256,  for  1  mo.  9  da.  83.   $226,  for  2  mo.  21  da. 

24.  $720,  for  3  mo.  12  da.  84.  $318,  for  2  mo.  21  da. 

25.  $863,  for  4  mo.  15  da.  35.  $108,  for  3  mo.  11  da. 

26.  $145,  for  46  da.  86.  $261,  for  4  mo.  9  da. 

27.  $258,  for  35  da.  87.  $182,  for  1  mo.  7  da. 

28.  $317,  for  92  da.  88.  $244,  for  27  da. 

29.  $412,  for  3  mo.  10  da.  39.  $368,  for  1  yr.  7  mo. 

30.  $651,  for  2  mo.  11  da.  Jfl.  $511,  for  1  yr.  14  da. 
81.  $115,  for  29  da. 

325.  To  find  the  interest  at  any  rate  per  cent,  find  the 

interest  at  6%,  divide  by  6,  and  multiply  by  the  given  rate. 


PROBLEMS 

Find  the  interest  on: 

1.  $516,  for  38  da.,  at  8%. 

2.  $1218,  for  3  mo.  14  da.,  at  5%. 
8.  $245.80,  for  4  mo.  18  da.,  at  7%. 

4.  $52.65,  for  1  mo.  12  da.,  at  3%. 

5.  $1071,  for  1  yr.  5  mo.  15  da.,  at  4%. 

6.  $293,  for  2  yr.  8  mo.  21  da.,  at 

7.  $364,  for  216  da.,  at  9%. 

8.  $1357,  for  83  da.,  at  2%. 

9.  $574,  for  33  da.,  at  5%. 
10.  $619,  for  72  da.,  at  7%. 


326.  Ordinary  Six  Per  Cent  Method 

TABLE 

Interest  on  $1,  for  1  yr.,    at  6%  =  $.06 

Interest  on  $1,  for  2  mo.,  at  6%  =  .01 

Interest  on  $1,  for  1  mo.,  at  6%  =  .005 

Interest  on  $1,  for  6  da.,  at  6%  =  .00.1 
Interest  on  $1,  for  1  da.,  at  6%  = 


186  MODERN    COMMERCIAL   ARITHMETIC 

7  mo. 


EXAMPLE.  —  Find   the   interest   on   $150,  for  2  yr. 
19  da.,  at  6%. 

SOLUTION 

Int.  on  $1  for    2  yr. 

=  $.12 

Int.  on  $1  for    7  mo. 

=    .035 

Int.  on  $1  for  18  da. 

=    .003 

Int.  on  $1  for    1  da. 

=    .OOOJ 

Int.  on  $1  for    2  yr.  7  mo.  19  da.  =  $.158| 
Int.  on  $150  for  2  yr.  7  mo.  19  da  =  150x  $.158£  =  $23.725 

PROBLEMS 

Find  the  interest,  at  6%,  on: 

1.  $575,  for  1  yr.  6  mo.  28.  $7259  for  1  yr.  6  mo.  8  da, 

2.  $640,  for  2yr.  4  mo.  12  da.  24.  $813,  for  2  yr.  7  mo. 

8.  $315,  for  1  yr.  3  mo.  9  da.  25.  $856,  for  1  yr.  6  mo.  14  da. 

4.  $720,  for  3  yr.  7  mo.  15  da.  26.  $921,  for  4  yr.  8  mo.  12  da. 

5.  $645,  for  1  yr.  18  da.  27.  $1040,  for  3  yr.  7  mo.  9  da. 

6.  $83,  for  2  yr.  11  mo.  28.  $623,  for  3  yr.  1  mo.  5  da. 

7.  $614,  for  9  mo.  23  da.  29.  $408,  for  2  yr.  11  mo. 

8.  $176,  for  10  mo.  27  da.         29  da. 

9.  $394,  for  1  yr.  25  da.  80.  $513,  for  4  yr.  3  mo.  12  da. 

10.  $261,  for  1  yr.  9  mo.  6  da.  81.  $719,  for  5  yr.  8  mo.  13  da. 

11.  $312,  for  3  yr.  2  mo.  11  da.  82.  $605,  for  4  yr.  9  mo.  4  da. 

12.  $511,  for  4  yr.  6  mo.  18  da.  83.  $352,  for  11  mo.  28  da. 
18.  $117,  for  5*mo.  13  da.  84.  $1423,  for  3  yr.  22  da. 

14.  $226,  for  114  da.  85.  $178,  for  2  yr.  10  mo. 

15.  $391,  for  226  da.  17  da. 

16.  $538,  for  107  da.  86.  $137,  for  1  yr.  5  mo.  25  da. 

17.  $264,  for  210  da.  87.  $386,  for  2  yr.  7  mo.  27  da. 

18.  $546,  for  72  da.  88.  $920,  for  1  yr.  11  mo. 

19.  $185,  for  49  da.  16  da. 

20.  $229,  for  95  da.  89.  $401,  for  2  yr.  3  mo.  26  da. 

21.  $927,  for  4  mo.  23  da.  40.  $738,  for  3  yr.  5  mo.  11  da. 

22.  $641,  for  1  yr.  19  da. 

327.  In  the  following  problems,  find  the  term  of  interest 
by  compound  subtraction. 

Solve  the  following  problems  by  your  choice  of  methods. 


INTEREST  187 

PROBLEMS 

Find  the  interest  and  amount  of : 

1.  $643,  from  Jan.  1,  1898,  to  July  16,  1898,  at  6%. 

2.  $718,  from  Dec.  13,  1899,  to  May  4,  1900,  at  8%. 

3.  $136,  from  April  6,  1899,  to  Oct.  28,  1899,  at  4%. 

4.  $207,  from  Jan.  3,  1898,  to  Sept.  27,  1898,  at  6%. 

5.  $1692,  from  Feb.  26,  1897,  to  Aug.  13,  1897,  at  5%. 

6.  $2046,  from  Sept.  30,  1898,  to  Feb.  13,  1899,  at  6%. 

7.  $251,  from  Dec.  18,  1896,  to  March  12,  1897,  at  3%. 

8.  $235,  from  May  29,  1899,  to  Oct.  3,  1899,  at  4%. 

9.  $2187,  from  Oct.  15,  1898,  to  Aug.  26,  1899,  at  5%. 

10.  $514,  from  Nov.  20,  1897,  to  June  28,  1898,  at  4£%. 

11.  $342,  from  Feb.  16,  1898,  to  June  1,  1900,  at  7%. 

12.  $634,  from  April  17,  1899,  to  Dec.  15,  1900,  at  3%. 
IS.  $738,  from  Jan.  1,  1898,  to  Sept.  5,  1899,  at  6%. 

14.  $1235,  from  Oct.  7,  1898,  to  May  10,  1899,  at  7%. 

15.  $2950,  from  Dec.  12,  1899,  to  July  6,  1900,  at  8%. 

16.  $965,  frcm  April  19,  1900,  to  Dec.  21,  1901,  at  5%. 

17.  $433,  from  July  21,  1899,  to  Dec.  16,  1899,  at  4%. 

18.  $1580,  from  Nov.  30,  1898,  to  March  17,  1899,  at  5%. 

19.  $875,  from  Aug.  15,  1899,  to  Nov.  5,  1900,  at  6%. 

20.  $386,  from  May  19,  1900,  to  Sept.  27,  1901,  at  8%. 

21.  $915,  from  June  2,  1899,  to  May  15,  1900,  at  5%. 

22.  $1023,  from  Feb.  8,  1898,  to  Aug.  25,  1899,  at  7%. 
2S.  $3607,  from  March  13,  1900,  to  April  20,  1901,  at  6%. 

24.  $619,  from  June  9,  1900,  to  May  14,  1902,  at  5%. 

25.  $785,  from  Nov.  7,  1900,  to  Jan.  1,  1902,  at  6%. 

Find  the  interest  and  amount  for  the  exact  number  of  days: 

26.  $315,  from  May  1,  1901,  to  June  14,  1901,  at  6%. 

27.  $427,  from  Sept.  4,  1901,  to  Nov.  1,  1901,  at  5%. 

28.  $1380,  from  June  18,  1901,  to  Aug.  3,  1901,  at  6%. 

29.  $1025,  from  Aug.  30,  1902,  to  Oct.  31,  1902,  at  8%. 
SO.  $716,  from  Oct.  17,  1902,  to  Dec.  8,  1902,  at  7%. 

31.  $824,  from  July  26,  1902,  to  Oct.  7,  1902,  at  6%. 

32.  $906,  from  Jan.  30,  1902,  to  March  4,  1902,  at  4£%. 

33.  $314,  from  April  1,  1901,  to  June  28,  1901,  at  6%. 


188  MODERN   COMMERCIAL    ARITHMETIC 

34.  $423,  from  Aug.  3,  1901,  to  Nov.  9,  1901,  at  7%. 

35.  $206,  from  Oct.  19,  1900,  to  Nov.  1,  1900,  at  6%. 

36.  $341,  from  Nov.  16,  1900,  to  Jan.  2,  1901,  at  8%. 

37.  $1217,  from  Feb.  4,  1901,  to  May  4,  1901,  at 

38.  $1087,  from  Nov.  1,  1901,  to  Jan.  27,  1902,  at 

39.  $421,  from  Jan.  2,  1902,  to  March  1,  1902,  at  7%. 

40.  $538,  from  Dec.  5,  1902,  to  Feb.  6,  1903,  at  4%. 

41.  $673,  from  Sept.  13,  1902,  to  Dec.  8,  1902,  at  5%. 

42.  $738,  from  Aug.  1,  1901,  to  Sept.  3,  1901,  at  3%. 

43.  $297,  from  Feb.  7,  1901,  to  April  4,  1901,  at  3J-%. 
44-  $309,  from  June  6,  1902,  to  Oct.  1,  1902,  at  4%. 

45.  $273,  from  April  3,  1901,  to  July  29,  1901,  at  6%. 

46.  $948,  from  July  4,  1902,  to  Sept.  3,  1902,  at  4|%. 

47.  $3071,  from  May  7,  1902,  to  Sept.  1,  1902,  at  5%. 

48.  $4253,  from  Nov.  9,  1901,  to  Jan.  1,  1902,  at  5£%. 

49.  $1406,  from  Jan.  7,  1902,  to  April  11,  1902,  at  8% 
60.  $2350,  from  July  29,  1902,  to  Dec.  1,  1902,  at 


328.  In  finding   the   interest   on  any   sum,  we   use   the 
formula  : 

Principal  x  rate  (for  time)  =  interest 

The  product  of  two  numbers  divided  by  one  of  them  is  the 
other  number.     Therefore, 

Interest  •*•  rate  (for  time)  =  principal 

Interest  •*•  principal  =  rate  (for  time) 

Kate  (for  time)  -*-rate  (per  annum)  =  time  (in  years) 

Eate  (for  time)  -*•  time  (in  years)  =  rate  (per  annum) 

Principal  x  (1  +  rate  for  time)  =  amount 

Amount  -*-  principal  =  (1  +  rate  for  time) 

Amount  •*-  (1  +  rate  for  time)  =  principal 

PROBLEMS 

1.  If  the  principal  is  $240,  the  rate  6%,  and  the  time  4 
mo.,  what  is  the  interest? 

2.  If  the  interest  is  $4.80,  the  principal  $240,  and  the  rate 
6%,  what  is  the  time? 


INTEREST  189 

8.  If  the  interest  is  $4.80,  the  principal  $240,  and  the  time 
4  mo.,  what  is  the  rate  per  annum? 

4-  Find  the  amount  of  $360,  for  8  mo.,  at  6%. 

5.  If  the  amount  is  $374.40,  the  principal  $360,  and  the 
time  8  mo.,  what  is  the  rate? 

6.  If  the  amount  is  $374.40,  the  principal  $360,  and  the 
rate  6  % ,  what  is  the  time? 

7.  If  the  amount  is  $374.40,  the  time  8  mo.,  and  the  rate 
6%,  what  is  the  principal? 

8.  How  long  must  I  loan  $80,  at  6%,  that  it  may  amount 
to  $100? 

9.  At  what  rate  per  cent  must  I  loan  $75  that  it  may  draw 
$1.87£  interest  in  6  mo.? 

10.  If  I  borrow  $245  for  9  mo.,  at  7%,  for  how  long  must 
I  loan  $315  at  6%  to  balance  the  favor? 

11.  How  long  will  it  take  a  sum  of  money  at  simple  inter- 
est to  double  itself  at  6%?  5%?  8%?  3%?  7%?  10%? 

12.  If  the  interest  is  $9.45,  the  principal  $315,  and  the 
time  8  mo.,  what  is  the  rate  per  annum? 

18.  In  how  long  will  $110  amount  to  $125  at  4%? 

14.  What  sum  will  amount  to  $580  at  6%  in  1  yr.  4  mo.? 

15.  At  what  rate  per  cent  must  $150  be  loaned  that  it  may 
amount  to  $175  in  2  yr.? 

16.  If  I  borrow  $525  for  1  yr.  4  mo.  at  5%,  how  long  must 
I  loan  $475  at  6  %  to  balance  the  favor? 

17.  At  what  per  cent  must  $340  be  loaned  to  gain  $28  in 
1  yr.  6  mo.? 

18.  What  sum  of  money,  invested  April  1,   1902,  at  6% 
interest,  will  amount  to  $1000  Jan.  1,  1904? 

19.  How  long  will  it  take  $100  to  double  itself  at  4|% 
simple  interest? 

20.  What  rate  of  interest  must  be  charged  in  order  that 
>  may  amount  to  $697.67  in  1  yr.  4  mo.? 


190  MODERN-   COMMERCIAL    ARITHMETIC 

PERIODIC  INTEREST 

329.  Simple  interest  is  simply  interest  on  the  principal. 

330.  Periodic  Interest  is  interest  on    the  principal   and 
interest  on  the  simple  interest  due  at  certain  interest  periods. 

331.  Interest  maybe  due  annually,  semi-annually,  quar- 
terly, etc. 

332.  Annual  Interest  is  interest  on  the  principal  payable 
annually,   and  simple  interest   on  the   interest   that   remains 
unpaid. 

333.  Semi- Annual  Interest  is  interest  on  the  principal  pay- 
able semi-annually,  and  simple  interest  on  the   interest  that 
remains  unpaid. 

334.  Quarterly  Interest  is  interest  on  the  principal  payable 
quarterly,  and  simple  interest   on  the  interest  that  remains 
unpaid. 

335.  In  some  States  periodic   interest   cannot  be  legally 
collected.     To    secure    periodic    interest,  a    contract    should 
specify  it. 

EXAMPLE  1. — Find  the  annual  interest  on  $500  for  4  yr.  at 
6%,  if  no  interest  is  paid  until  the  principal  is  due. 

SOLUTION 
Int.  on  $500  for  1  yr.  =  $  30 

Int.  on  $500  for  4  yr.  =    120 

Int.  on  $30  (unpaid  int.)  for  3  yr.,  2  yr., 

and  1  yr.,  or  for  6  yr.  =      10.80 

Annual  int.  =  $130.80 

EXAMPLE  2. — What  is  the  semi-annual  interest  on  $400  for 
3  yr.  4  mo.,  at  6%? 

SOLUTION 

Int.  on  $400  for  6  mo.  =  $12 

Int.  on  $12  for  2  yr.  10  mo.,  2  yr.  4  mo., 
1  yr.  10  mo.,  1  yr.  4  mo.,  10  mo., 
and  4  mo.,  or  for  9  yr.  6  mo.  =  6.84 

Int.  on  $400  for  3  yr.  4  mo.  =    80 

Semi-annual  int.  =  $86.84 


INTEREST  191 

PROBLEMS 

1.  What  is  the  annual  interest  on  $475,  for  4  yr.  8  mo. ,  at  6  % ? 

2.  Find  the  semi-annual  interest  on  $263,  for  2  yr.  7  mo., 
at  6%. 

3.  Find  the  amount  of  interest  due  at  the  end  of  5  yr. 
3  mo.,  on  a  note  for  $218,  at  6%  annual  interest. 

4.  What  will  $125  amount  to  in  2  yr.  8  mo.,  with  interest 
at  8%,  payable  quarterly? 

5.  Find  the  annual  interest  on  $436,  for  5  yr,.  8  mo.,  at  5%. 

6.  Find  the  semi-annual  interest  on  $1080,  for  2  yr.  7  mo. 
15  da.,  at  5%. 

7.  What  will  $125  amount  to  in  1  yr.  9  mo.  12  da.,  with 
quarterly  interest,  at  6%? 

8.  Find  the  amount  of  $528  for  2  yr.  9  mo.  18  da.,  with 
interest  at  4%,  payable  semi -annually. 

9.  What  will  be  the  annual  interest  on  $1750  for  3  yr. 
11  mo.  8  da.,  at  4£%? 

10.  Find  the  amount  of  $318  for  2  yr.  5  mo.  21  da.,  at  6% 
interest,  payable  semi- annually. 

11.  What  will  $162  amount  to  in  1  yr.  10  mo.  25  da.,  at 
5%  quarterly  interest? 

12.  What  will  be  the  amount  of  $435  for  4  yr.  8  mo.,  at 
4J%  annual  interest? 

18.  What  sum  will  amount  to  $500  in  1  yr.  8  mo.,  at  6% 
semi-annual  interest? 

COMPOUND  INTEREST 

336*  Compound  Interest  is  interest  upon  the  principal  and 
on  the  interest  combined  with  the  principal  at  regular  intervals. 

For  the  purpose  of  finding  the  compound  interest,  the  sim- 
ple interest  is  added  to  the  principal  at  regular  intervals,  and 
the  amount  becomes  the  new  principal  on  which  the  interest  is 
computed. 

Interest  may  be  compounded  annually,  semi-annually,  or 
quarterly. 

337.  Compound  interest  cannot  be  enforced  by  law. 

Savings  banks  usually  allow  compound  interest. 


192  MODERN   COMMERCIAL  ARITHMETIC 

EXAMPLE. — Find  the  interest  on  $250  for  2  yr.  6  mo.  15  da., 
at  6%,  compounded  annually. 

SOLUTION 
$250       =  prin. 

15          int.  for  first  year 

$265       =  amt.  for  first  year 
15.90  =  int.  for  second  year 

$280.90  =  amt.  for  second  year 
9.13  =  int.  for  6  mo.  15  da. 
$290.03  =  amt.  for  2  yr.  6  mo.  15  da. 

250       =  original  prin. 
$  40.03  =  compound  int. 

NOTES. — 1.  As  in  the  above  example,  the  last  interest  period  may 
be  but  part  of  a  full  period. 

2.  If  interest  is  compounded  semi-annually  or  quarterly,  take  one- 
half  or  one-fourth  of  the  annual  rate  per  cent. 


PROBLEMS 

1.  What  is  the  interest  on  $640  for  2  yr.  8  mo.,  at  7%,  com- 
pounded semi-annually? 

2.  What  is  the  interest  on  $1230  for  1  yr.  3  mo.  15  da.,  at 
8%,  compounded  quarterly? 

8.  Find  the  interest  on  $390  for  3  yr.  7  mo.,  at  5%,  com- 
pounded annually. 

4.  Find  the  amount  of  $750  for  2  yr.  9  mo.  18  da.,  with 
6%  interest,  compounded  annually. 

5.  Find  the  interest  on  $375  for  6  yr.  8  mo.,  at  5%,  com- 
pounded annually. 

6.  Find  the  amount  of  $520  for  3  yr.  9  mo.,  at  8%  inter- 
est, compounded  semi-annually  < 

7.  What  is  the  interest  on  $640  for  2  yr.  3  mo.,  at  10% 
interest,  compounded  quarterly? 

8.  What  is  the  amount  of  $328  for  7  yr.  4  mo.,  at  5%  inter- 
est, compounded  annually? 


INTEREST 


193 


Compound  Interest  Table 

338.  Persons  who  have  to  make  many  computations  in 
compound  interest  usually  use  a  printed  table  like  the  following : 

TABLE  SHOWING  THE  AMOUNT  OF  $1  AT  COMPOUND  INTEREST 


1TEAR 

2?o 

S£ 

4^ 

5^ 

6# 

7J6 

1. 

1.020000 

1.030000 

1040000 

1.050000 

1.060000 

1.070000 

2. 

1.040400 

1.060900 

1.081600 

1.102500 

1.123600 

1.144900 

3. 

1.061208 

1.092727 

1.124864 

1.157625 

1.191016 

1.225043 

4. 

1.082432 

1.125508 

1.169858 

1.215506 

1.262477 

1.310796 

5. 

1.104080 

1.159274 

1.216652 

1.276281 

1.338225 

1.402551 

6. 

1.126162 

1.194052 

1.265319 

1.340095 

1.418519 

1.500730 

7. 

1.148685 

1.229873 

1.315931 

1.407100 

1.503630 

1.605781 

8. 

1.171659 

1.266770 

1.368569 

1.477455 

1.593848 

1.718186 

9. 

1.195092 

1.304773 

1.423311 

1.551328 

1.689479 

1.838459 

10. 

1.218994 

1.343916 

1.480244 

1.628894 

1.790847 

1.967151 

11. 

1.243374 

1.384233 

1.539454 

1.710339 

1.898298 

2.104852 

12. 

1.268241 

1.425760 

1.601032 

1.795856 

2.012196 

2.252191 

13. 

1.293606 

1.468533 

1.665073 

1.885649 

2.132928 

2.409845 

14. 

1.319478 

1.512589 

1.731676 

1.979931 

2.260904 

2.578534 

15. 

1.345868 

1.557967 

1.800943 

2.078928 

2.396558 

2.759031 

16. 

1.372785 

1.604706 

1.872981 

2.182874 

2.540351 

2.952163 

17. 

1.400241 

1.652847 

1.947900 

2.292018 

2.692772 

3.158815 

18. 

1.428246 

1.702433 

2.025816 

2.406619 

2.854339 

3.379932 

19. 

1.456811 

1.753506 

2.106849 

2.526950 

3.025599 

3.616527 

20. 

1.485947 

1.806111 

2.191123 

2.653297 

3.207135 

3.869684 

NOTES. — 1.  Any  principal  multiplied  by  the  amount  of  $1  for  any 
given  time,  at  any  given  rate,  is  the  amount  of  the  principal,  for  the 
given  time  and  rate. 

2.  The  amount  of  $1  for  any  given  number  of  years  is  equal  to  the 
product  of  the  amounts  of  $1,  for  such  periods  of  years  whose  sum  is 
equal  to  the  given  number  of  years.     To  find  the  amount  of  $1  for 
40  yr.,  multiply  together  the  amounts  for  20  and  20  yr.,  or  for  15,  15, 
and  10  yr.,  etc. 

3.  For  semi-annual  interest,  take  |  the  rate  for  twice  the  time. 

4.  For  quarterly  interest,  take  \  the  rate  for  4  times  the  time. 

PROBLEMS 

Solve  the  following  problems  by  the  use  of  the  table: 

1.  Find  the  compound  interest  on  $632,  for  15  yr.,  at  5%. 

2.  Find  the  interest  on  $1285,  forv9  yr.  9  mo.,  at  6%, 
compounded  semi-ammally. 

3.  Find  the  amount  of  $750,  for  3  yr.  8  mo.,  at  8%,  com- 
pounded quarterly. 


194 


MODERN    COMMERCIAL   ARITHMETIC 


4.  What  is  the  interest  on  $196,  for  16  yr.  5  mo.,  at  6%, 
compounded  annually? 

5.  What  is  the  amount  of  $224,  for  6  yr.  8  mo.,  at  8% 
interest,  compounded  semi- annually? 

6.  Find  tho  amount  of  $3567,  for  3  yr.  6  mo.,  at  4%,  com- 
pounded semi-annually. 

7.  What  is  the  interest  on  $2687,  for  7  yr.  9  mo.  15  da.,  at 
5%,  compounded  annually? 

Find  the  compound  interest  on: 


PRINCIPAL 

RATE 

8.  $1428 

8% 

9.  $  732 

7% 

10.  $  523 

6% 

11.  $  176 

12% 

12.  $  391 

5% 

13.  $  746 

3% 

14*  $  412 

4% 

15.  $  834 

4% 

TIME 

9  yr.  7  mo. 
14  yr.  10  mo. 
24  yr. 

5  yr. 

7  yr. 
35  yr. 
16  yr. 


9  mo. 


14  yr. 


8  mo. 
5  mo. 


PAYABLE 
quarterly 
annually 
annually 
quarterly 
semi-annually 
annually 
annually 
semi-annually 


Compound  Interest  Amount  Table 

TABLE  SHOWING  THE  AMOUNT  OF  $1  INVESTED  AT  THE  BEGINNING  OF 
EACH  YEAR  FOR  A  SERIES  OF  YEARS,  AT  COMPOUND  INTEREST 


YEAR 

%% 

2*0 

80 

8W 

4£ 

W 

1. 

1.020000 

1.025000 

1.030000 

1.035000 

1.040000 

1.045000 

2. 

2.060400 

2.075625 

2.090900 

2.106225 

2.121600 

2.137025 

3. 

3.121608 

3.152515 

3.183627 

3.214942 

3.246464 

3.278191 

4. 

4.204040 

4.256328 

4.309135 

4.362465 

4.416322 

4.470709 

5. 

5.308120 

5.387736 

5.468409 

5.550152 

5.632975 

5.716891 

6. 

6.434283 

6.547430 

6.662462 

6.779407 

6.8982S4 

7.019151 

7. 

7.582969 

7.736115 

7.892336 

8.051686 

8.214226 

8.380013 

8. 

8.754628 

8.954518 

9.159106 

9.368495 

9.582795 

9.802114 

9. 

9.949721 

10.203381 

10.463879 

10.731393 

11.006107 

11.288209 

10. 

11.168715 

11.483466 

11.807795 

12.141991 

12.486351 

12.841178 

11. 

12.412089 

12.795552 

13.192029 

13.601961 

14.025805 

14.464031 

12. 

13.680331 

14.140441 

14.617790 

15.113030 

15.626837 

16.159913 

13. 

14.973938 

15.518952 

16.086324 

16.676986 

17.291911 

17.932109 

14. 

16.293416 

16.931926 

17.598913 

18.295680 

19.023587 

19.784054 

15. 

17.639285 

18.380224 

19.156881 

19.971029 

20.824531 

21.719336 

16. 

19.012070 

19.864730 

20.761587 

21.705015 

22.697512 

23.741706 

17. 

20.412312 

21.386348 

22.414435 

23.499691 

24.645412 

25.855083 

18. 

21.840558 

22.946007 

24.116868 

25.357180 

26.671229 

28.063562 

19. 

23.297369 

24.544657 

25.870374 

27.279681 

28.778078 

30.371422 

20. 

24.783317 

26.183273 

27.676485 

29.269470 

30.969201 

32.783136 

INTEREST 

COMPOUND  INTEREST  AMOUNT  TABLE. — Continued. 


195 


YEAR 

Z% 

6£ 

1% 

8£ 

§% 

10£ 

1.... 

1.050000 

1.060000 

1.070000 

1.080000 

1.090000 

1.100000 

2.... 

2.152500 

2.183600 

2.214900 

2.246400 

2.278100 

2.310000 

3.... 

3.310125 

3.374616 

3.439943 

3.506112 

3.573129 

3.641000 

4.... 

4.525631 

4.637093 

4.750739 

4.866601 

4.984710 

5.105100 

5.... 

5.801912 

5.975318 

6.153290 

6.335929 

6.523334 

6.715610 

6.... 

7.142008 

7.393837 

7.654021 

7.902803 

8.200434 

8.487171 

7.... 

8.549108 

8.897468 

9.259802 

9.616627 

10.028473 

10.435888 

8.... 

10.026564 

10.491316 

10.977988 

11.467557 

12.021036 

12.579476 

9.... 

11.577892 

12.180795 

12.816448 

13.466562 

14.192929 

14.937424 

10.... 

13.206787 

13.971642 

14.783599 

15.625487 

16.560293 

17.531167 

11.... 

14.917126 

15.869941 

16.888451 

17.957126 

19.140719 

20.384283 

12.... 

16.712982 

17.882137 

19.140963 

20.475296 

21.953384 

23.522712 

13.... 

18.598631 

20.015066 

21.550488 

23.194920 

25.019189 

26.974983 

14.... 

20.578563 

22.275970 

24.129022 

26.132113 

28.360916 

30.772481 

15.... 

22.657491 

24.672528 

26.888053 

29.304283 

32.003398 

34.949729 

16.... 

24.840366 

27.212880 

29.840217 

32.730225 

35.973704 

39.544702 

17.... 

27.132384 

29.905652 

32.999032 

36.430243 

40.301338 

44.599173 

18.... 

29.539003 

32.759992 

36.378965 

40.426263 

45.018458 

50.159090 

19.... 

32.065954 

35.785591 

39.995492 

44.741964 

50.160119 

56.275029 

20.... 

34.719251 

38.992727 

43.865177 

49.402921 

55.764530 

63.002529 

NOTES 

339.  A  Note,  or  a  Promissory  Note,  is  a  written  promise  to 
pay  a  sum  certain,  at  a  time  certain. 

The  sum  may  be  paid  in  money,  or  in  other  valuable  things, 
as  mentioned  in  the  note. 

The  time  of  payment  may  be  a  fixed  date  (as  June  1,  1903) ;  it 
may  be  the  date  of  the  occurrence  of  an  event  that  is  sure  to  hap- 
pen (as  the  death  of  a  person) ;  it  may  be  any  date  on  which  the 
person  entitled  to  payment  may  ask  for  it  (payment  on  demand). 

340.  Form  of  Notes 

1450.00.  Buffalo,  N.  Y.,  June  1,  1902. 

Six  months  after  date,  for  value  received,  I  promise 
to  pay  T.  B.  Smith,  or  order,  four  hundred  fifty  dol- 
lars ($450.00).  D.  A.  WEST. 

$500.80.  Detroit,  Mich.,  June  1,  1902. 

Four  months  after  date,  for  value  received,  I  prom- 
ise to  pay  R.  L.  Gordon,  or  bearer,  five  hundred  j80°0 
dollars  ($500.80),  with  6  per  cent  interest. 

WALTER  JOHNSON. 


196  MODERN    COMMERCIAL-  ARITHMETIC 

341.  The  Maker  or  Drawer  is  the  person  who  signs  the 
note. 

342.  The  Payee  is  the  person  to  whom  the  note  is  made 
payable. 

343.  The  Face  of  the  note  is  the  sum  promised  to  be  paid. 

344.  A  note  should  contain: 

1.  Time  when,  and  place  where  made. 

2.  Time  when  payable. 

3.  The  sum  to  be  paid. 

4.  The  expression,  "for  value  received." 

To  prevent  forgery  the  sum  to  be  paid  should  be  written 
in  words. 

If  the  words  "for  value  received"  are  omitted,  the  maker 
cannot  be  compelled  to  pay  unless  the  owner  of  the  note  can 
show  that  the  maker  received  a  valuable  consideration  for  mak- 
ing the  note. 

If  no  place  of  payment  is  mentioned,  the  note  is  payable  at 
the  maker's  place  of  business. 

A  note  may  be  made  payable  "on  demand,"  and  is  then 
payable  whenever  its  owner  calls  for  its  payment. 

345.  A  note  may  contain: 

1.  The  words  "or  order,"  or  "or  bearer." 

2.  The  words  "with  interest,"  or  "with  use." 

If  the  words  "with  interest,"  or  "with  use,"  are  omitted, 
the  note  will  not  draw  interest,  but  if  it  is  not  paid  at  matu- 
rity, it  will  draw  interest  at  the  legal  rate  from  the  time  it 
becomes  due. 

If  a  note  contains  the  words  "with  interest,"  but  does  not 
mention  the  rate,  it  will  draw  interest  at  the  legal  rate  where 
the  note  was  made. 

If  a  note  contains  the  words  "or  bearer,"  it  is  payable  to 
whoever  presents  it  for  payment. 

If  a  note  contains  the  words  "or  order,"  it  is  payable  to  the 
person  mentioned  as  payee,  or  to  whomever  he  orders  it  to  be 


INTEREST  197 

paid.     A  payee  may  order  a  note  paid  to  another  by  indorse- 
ment. 

346.  An  Indorsement  is  a  writing  on  the  back  of  a  docu- 
ment. 

347.  A  note  may  be  indorsed: 

1.  To  make  it  payable  to  another  person. 

2.  To  make  sure  that  the  note  will  be  paid. 

3.  To  show  that  the  note  has  been  paid. 

4.  To  show  that  a  partial  payment  has  been  made. 

Men  frequently  buy  and  sell  notes.  If  a  note  is  made  pay- 
able to  J.  Smith,  or  bearer,  Smith  may  sell  it  to  another  per- 
son, who  may  also  sell  it.  The  maker  will  pay  whoever 
presents  the  note  for  payment.  But,  if  T.  Jones,  who  buys 
the  note  of  Smith,  thinks  that  the  maker  is  not  "good"  for  the 
amount  of  the  note,  he  may  require  Smith  to  indorse  the  note 
by  writing  his  name  on  the  back  of  it.  That  would  legally 
bind  Smith  to  pay  the  note  in  case  the  maker  should  refuse  to 
pay  it  if  proper  demand  were  made  for  its  payment. 

If  a  note  is  made  payable  to  "J.  Smith,  or  order,"  and 
Smith  sells  the  note  to  Jones,  Smith  may  write  on  the  back  of 
the  note,  "Pay  to  Jones. — J.  Smith."  The  note  is  said  to  be 
transferred  to  Jones,  and  is  payable  to  him.  Smith,  by  his 
indorsement,  is  responsible  for  the  payment  of  the  note  if  the 
maker  refuses  to  pay  Jones. 

When  a  note  is  paid,  it  is  returned  to  the  maker,  who  may 
destroy  it.  But  the  destruction  of  a  note  is  no  proof  that  it  has 
been  paid.  If  a  note  is  lost,  the  payee  may  still  require  the 
maker  of  the  note  to  pay  the  debt. 

When  a  note  is  paid,  unless  it  is  made  payable  to  the 
bearer,  the  maker  often  requires  the  holder,  or  owner,  to  write  his 
name  on  the  back,  which  makes  the  note  payable  to  the 
maker.  The  maker  then  has  the  indorsed  note  as  a  receipt  to 
show  that  it  has  been  paid. 

A  treasurer  who  pays  out  money  on  the  order  of  some  other 
person  should  always  require  the  payee  of  an  order  to  indorse  it. 
It  then  becomes  a  receipt  for  the  treasurer. 


198  MODERN    COMMERCIAL   ARITHMETIC 

If  a  part  payment  is  made  on  a  note,  the  payee  writes  on 
the  back  of  the  note,  above  his  name,  a  statement  of  the 
amount  received  in  payment. 

348.  The  person  who  writes  his  name  on  the  back  of  a 
note  is  an  Indorser. 

349.  A  note  may  be  indorsed  in  one  of  three  ways : 

1.  The  payee  may  write  only  his  name  on  the  back  of  the 
note. 

That  makes  the  note  payable  to  the  bearer,  and  also  makes 
the  indorser  liable  for  its  payment  if  the  maker  refuses  to  pay 
it.  This  is  called  indorsement  "in  blank." 

2.  The  payee  may  write,  "Pay  to  James  Wise,"  and  sign 
his  name. 

That  makes  the  note  payable  to  James  Wise,  and  also  makes 
the  indorser  responsible  for  its  payment.  This  is  called 
a  "full  indorsement." 

The  payee  may  indorse  a  note  thus:  "Pay  to  James  Wise, 
or  order. — J.  Smith."  James  Wise  may  indorse  the  note  in  a 
similar  manner  in  favor  of  Wilson  Niles,  and  so  on.  A  note 
may  have  several  indorsers,  each  01  whom  becomes  individually 
responsible  for  its  payment. 

An  indorsement  to  transfer  a  note  makes  the  indorser 
responsible  for  payment  unless  the  indorsement  is  made  "with- 
out recourse." 

3.  If  the  payee  wishes  to  transfer  a  note,  but  does  not  wish 
to   become   responsible   for    its   payment  except  to  a  limited 
degree,  he  may  indorse  the  note  thus:  "Pay  to  K.  A.  Wall,  or 
order,    without   recourse    to    me. — Anson  Brown."      This   is 
called  indorsement  "without  recourse." 

350.  A  note  may  be  indorsed  for  transfer,  for  security,  or 
for  transfer  and  security.     Write  and  indorse  notes  that  will 
illustrate  each  of  these. 

351.  If  the  maker  of  a  note  refuses  to  pay  it,  he  is  said  to 
dishonor  the  note. 

In  order  to  make  an  indorser  legally  responsible  for  the 
payment  of  a  note  that  has  been  dishonored  by  its  maker,  the 


INTEREST  199 

holder  of  the  note  must  demand  payment  of  its  maker  at 
maturity,  and  give  the  indorser,  within  a  reasonable  time, 
notice  of  its  dishonor  by  its  maker.  If  there  are  several 
indorsers,  each  should  be  notified. 

Notice  may  be  given  to  the  indorser  by  letter  or  verbally. 
If  the  parties  to  the  note  are  of  different  States,  the  owner  of 
the  note  should  mail  a  protest  to  the  indorser.  A  protest  is  a 
written  statement,  made  by  an  officer  who  takes  oaths,  giving 
notice  to  the  indorser  of  the  note  that  it  has  not  been  paid. 

352.  A  note  that  may  be  transferred  from  one  party  to 
another  by  indorsement  and  give  the  holder  the  right  to  sue  for 
its  payment  in  his  own  name  is  a  Negotiable  Note. 

Such  a  note  must  contain  the  words  "or  order,"  "bearer," 
or  "or  bearer." 

353.  A  note  that  cannot  be  transferred  by  indorsement  is 
a  Non-Negotiable  Note.     A  note  made  payable  to  James  Smith 
is  not  negotiable. 

354.  In  some  States  three  days  are  allowed  by  law  for  the 
payment  of  a  note  in  addition  to  the  time  mentioned  in  the 
note.     These  three  days  are  called  Days  of  Grace. 

355.  A  note  given  for  a  number  of  months  is  due  on  the 
expiration  of  that  number  of  calendar  months.     Thus,  a  note 
given  on  February  1,  for  three  months,  is  due  May  1. 

356.  A  note  given  for  a  number  of  days  is  due  on  the 
expiration  of  that  number  of  days.     Thus,  a  note  given  on 
February  1,  for  ninety  days,  is  due  on  May  2  in  an  ordinary 
year,  and  on  May  1  in  a  leap  year. 

357.  A  note  maturing  on  a  legal  holiday  should  be  paid  on 
the  day  previous.     If  that  day  is  a  legal  holiday  also,  the  note 
should  be  paid  on  the  day  before.     If  Monday  is  a  legal  holi- 
day, notes  maturing  on  that  day  should  be  paid  on  Saturday. 

In  a  State  where  days  of  Grace  are  not  allowed,  if  the  day 
of  maturity  of  a  contract  falls  on  Sunday  or  a  holiday,  it  is  due 
the  day  following. 

358.  In  all  States  a  note  or  a  closed  account  will  out- 
law— become  void — in  a  certain  number  of  years  after  it  becomes 
due,  if  nothing  be  paid  on  it.     The  time  required  for  a  note  or 
an  account  to  outlaw  varies  in  the  different  States  from  two 
years  to  twenty  years. 


200 


MODERN   COMMERCIAL   ARITHMETIC 


359.  What  is  the  value  of  a  note  at  its  maturity? 

If  it  does  not  draw  interest,  its  value  is  its  face. 

If  it  draws  interest,  its  value  is  its  face  plus  the  interest. 

All  notes  draw  interest  after  they  become  due. 


PROBLEMS 

1.  Find  the  value  of  this  note  at  maturity : 

$263.80.  Rochester,  N.  Y.,  May  1,  1902. 

Four  months  after  date,  for  value  received,  I  prom- 
ise to  pay  Thomas  Byron,  or  order,  two  hundred  sixty- 
three  r%°o  dollars,  with  interest  at  6  per  cent. 

L.  C.  JOHNSON. 

2.  Find  the  amount  due  on  this  note  Sept.  1,  1903: 

$480.00.  Cleveland,  Ohio,  Jan.  17,  1902. 

Six  months  after  date,  I  promise  to  pay  A.  C.  Berry, 
or  order,  four  hundred  eighty  dollars,  for  value  re- 
ceived with  interest.  M.  F.  SWAN. 

NOTE. —  When  interest  is  mentioned  but  no  rate  is  given  in  these 
problems,  Q%  is  to  be  understood. 

Below  are  given  the  data  of  several  notes.  Find  the  due 
date  arid  the  amount  due  at  time  of  settlement,  assuming  that 
interest  is  at  6%,  and  that  no  interest  is  paid  till  the  time  of 
settlement : 

SETTLEMENT 
Oct.       6,  1902 
when  due 
Sept.  30,  1901 
Feb.  14,  1900 
5  mo.  after  date 
June  16,  1901 
Aug.  30,  1902 
Dec.  16,  1900 
April  1,  1901 
Nov.  25,  1900 


FACE 

DATE 

TIME 

3. 

$  625 

Jan. 

3, 

1900 

3 

mo. 

4. 

$  590. 

50 

Feb. 

12, 

1898 

90 

da. 

5. 

$  268. 

25 

Dec. 

7, 

1899 

6 

mo. 

6. 

$1120 

Oct. 

3, 

1897 

1 

F- 

7. 

$  375. 

60 

May 

5, 

1898 

60 

da.* 

8. 

$  214. 

75 

Nov. 

28, 

1899 

30 

da. 

9. 

$3620 

July 

29, 

1899 

4 

mo.* 

10. 

$  493 

March 

30, 

1898 

9 

mo.* 

11. 

$  318 

Sept. 

1, 

1899 

3 

mo. 

12. 

$  422 

April 

3, 

1900 

30 

da. 

*Interest  is 

not  mentioned 

in  the 

note. 

PARTIAL  PAYMENTS  201 

PARTIAL  PAYMENTS 

36O.  Payment  of  a  portion  of  the  amount  due  on  a  note 
is  often  made.  Such  a  payment  is  called  a  Partial  Payment. 

Several  partial  payments  are  often  made  on  a  note. 

The  amount  and  date  of  each  payment  should  be  indorsed 
on  the  back  of  the  note. 

Partial  payments  may  be  made  on  mortgages  and  accounts, 
and  may  be  made  before  or  after  the  obligation  becomes  due. 


361.  Mercantile  Rule 

MENTAL  PROBLEMS 

1.  What  will  a  debt  of  $500  amount  to  in  6  mo.,  interest  at 
6%?     If  $200  be  paid  4  mo.  before  the  debt  is  finally  paid,  to 
what  will  the  partial  payment  amount  at  the  time  of  settlement? 
If  such  a  payment  be  made,  what  will  be  the  net  amount  due 
on  the  note  at  the  end  of  6  mo.? 

2.  A  debt  of  $1000  was  settled  1  yr.  after  it  became  due,  but 
3  mo.  after  it  became  due  $200  was  paid  on  it,  and  3  mo.  later 
$400  was  paid  on  it.  What  was  the  amount  of  the  original  debt 
at  date  of  settlement,  interest  at  6%?     What  was  the  amount 
of  each  payment  at  date  of  settlement?     What  was  the  amount 
left  to  be  paid  at  the  time  of  settlement? 

Principles. — 1.  The  amount  of  the  debt  equals  the  face  of 
the  debt  plus  the  interest  on  the  same  till  the  time  of  settle- 
ment. , 

2.  The  amount  of  each  payment  equals  the  face  of  the  pay- 
ment plus  the  interest  on  the  same  till  the  time  of  settle- 
ment. 

3.  The  amount  due  at  the  time  of  settlement  equals  the 
amount  of  the  debt  less  the  sum  of  the  amounts  of  the  pay- 
ments. 

EXAMPLE. — The  following  payments  were  made  on  a  note 
dated  Jan.  1,  1900,  for  $500,  with  6%  interest:  April  3,  1900, 


202 


MODERN    COMMERCIAL   ARITHMETIC 


);  May  12, 1900,  $80;  June  25, 1901,  $90.     What  remained 
due  July  15,  1902? 

EXPLANATION. — Write  the  dates  in  consecutive  order,  putting  the 
last  first.  Begin  at  the  bottom  and  subtract  each  date  from  the  one 
immediately  above  it,  and  place  the  remainders  in  consecutive  order. 
Write  the  amounts  of  the  payments  and  the  debt  opposite  the  dates. 
Figure  the  interest  and  find  the  balance  due  as  shown  in  the  operation. 


OPERATION 


Subtraction  of  Dates 

Cr. 

Dr. 

Yr. 

Mo. 

Da. 

P'm'ts 

Int. 

Debt 

Int. 

1898 

7 

15 

time  of  settlement 

1897 

6 

25 

time  of  third  payment 

$  90.00 

1896 
1896 
1896 

5 
4 
1 

12 
3 

1 

time  of  second  payment 
time  of  first  payment 
time  of  note 

80.00 
240.00 

$500.00 

2 

6 

14 

time  from  note  to  settlement 

$240.00 

$32.88 

$500.00 

$76.17 

2 
2 

3 
2 

12 
3 

time  from  first  p'm't  to  settlem't 
time  from  second  p'm't  to  settlem't 

80.00 
90.00 

10.44 
5.70 

1 

0 

20 

time  from  third  p'm't  to  settlem't 

$410.00 

$49.02 

$500.00 

$76.17 

49.02 

76.17 

$459.02 

$576.17 

459.02 

Amount  due 

$1.7.15 

PROBLEMS 

1.  What  was  the  balance  due  Sept.  14,  1900,  on  a  note  for 
3,  dated  March  6,  1896,  interest  at  6%,  if  the  following 

payments  were  made:  Dec.  3,  1896,  $115;  Feb.  12,  1897,  $120; 

Oct.  18,  1898,  $208? 

&     $975.50.  New  York  City,  Jan.  14,  1897. 

Six  months  after  date  I  promise  to  pay  L.  C.  Stone, 
or  order,  nine  hundred  seventy -five  ffo  dollars,  for 
value  received,  with  interest  at  6  per  cent. 

C.  E.  BABCOCK. 

Find  the  amount  due  on  the  above  note  Jan.  1,  1900,  the 
following  payments  having  been  made:  Aug.  3, 1897,  $86;  Jan. 
12,  1898,  $175;  Dec.  23,  1898,  $215;  July  5,  1899,  $328. 


PARTIAL   PAYMENTS  203 

8.    $1285.00.  Philadelphia,  Pa.,  May  2,  1898. 

Four  months  after  date,  for  value  received,  1  prom- 
ise to  pay  to  the  order  of  G.  W.  Beam  twelve  hundred 
eighty-five  dollars.  A.  T.  BRONSON. 

The  note  was  not  paid  when  due,  but  the  following  pay- 
ments were  made:  Oct.  4,  1898,  $164;  Jan.  13,  1899,  $245; 
July  6,  1899,  $338.  What  remained  due  Sept.  23,  1899, 
money  being  worth  6%? 

4.  Find  the  balance  due  Oct.  28,  1902,  on  a  mortgage  given 
Nov.  1,  1897,  for  $2600,  interest  at  6%,  the  following  pay- 
ments having  been  made:  July  5,  1898,  $685;  Oct.  14,  1899, 
$1260;  March  7,  1900,  $240;  May  1,  1901, 


The  United  States  Rule 

362.  The  mercantile  rule  is  often  used  by  common  consent 
in  settling  short-time  notes  and  accounts. 

The  rule  sanctioned  by  the  Supreme  Court  of  the  United 
States  is  called  the  United  States  Kule.  The  principle  of  the 
United  States  Rule  is  that  each  payment  should  be  applied  to 
pay  the  interest  due  at  that  time,  and  the  balance  of  the  pay- 
ment should  be  used  to  diminish  the  principal.  If  at  any  time 
the  payment  is  less  than  the  amount  of  interest  due,  the  pay- 
ment is  not  considered  made  at  that  time,  but  it  is  added  to 
the  next  payment  or  payments,  when  the  sum  of  the  payments 
shall  at  least  equal  the  interest  due  at  the  date  of  last  payment. 

Most  States  have  adopted  the  United  States  Rule. 

MENTAL  PROBLEM 

On  Jan.  1,  I  owe  $1000.  How  much  will  I  owe  May  1, 
interest  at  6%?  If  on  May  1,  I  pay  $120,  how  much  will  I  still 
owe  on  that  date?  How  much  will  I  owe  Nov.  1?  If  I  pay 
$177  on  Oct.  1,  how  much  will  I  still  owe?  How  much  will  I 
owe  on  the  first  of  the  next  March? 

EXAMPLE. — A  mortgage  was  given  Jan.  12, 1896,  for  $6820, 
with  interest  at  6%.  The  following  payments  were  made: 


204  MODERN    COMMERCIAL   ARITHMETIC 

Oct.  15,  1896,  $380;  Feb.  17,  1897,  $650;  July  13,  1897, 
$760;  Jan.  15,  1898,  $1290.  How  much  remained  due  Nov. 
1,  1898? 

OPERATION 
Subtraction  of  Dates 

Year         Month        Day 

1898  11  1  time  of  settlement 

1898  1  15  time  of  fourth  payment 

1897  7  13  time  of  third  payment 

1897  2  17  time  of  second  payment 

1896  10  15  time  of  first  payment  Debt 

1896  7  12  time  mortgage  was  given  $6820.00 

Payment 

i  time  from  mortgage  to  first  payment      $380.00 

4  2  time  from  first  to  second  payment  650.00 

4  26  time  from  second  to  third  payment  760.00 

6  2  time  from  third  to  fourth  payment  1290.00 

9  16  time  from  fourth  payment  to  settlement 

Face  of  debt $6820.00 

Int.  to  first  payment 105.71 

Amt.  of  debt  at  first  payment $6925.71 

First  payment 380.00 

Amt.  of  debt  after  first  payment $6545.71 

Int.  to  second  payment 133.09 

Amt.  due  at  second  payment $6678.80 

Second  payment 650.00 

Amt.  due  after  second  payment $6028.80 

Int.  to  third  payment 146. 70 

Amt.  due  at  third  payment $6175.50 

Third  payment 760.00 

Amt.  due  after  third  payment $5415.50 

Int.  to  fourth  payment 164.27 

Amt.  due  at  fourth  payment $5579.77 

Fourth  payment 1290.00 

Amt.  due  after  fourth  payment $4289.77 

Int.  to  time  of  settlement 204.48 

Amt.  due  at  settlement $4494.25 


PROBLEMS 

1.  On  a  debt  of  $3245,  beginning  Sept.  3,  1897,  and  bearing 
5%  interest,  the  following  payments  were  made:  Jan.  14, 1898, 
$630;  Aug.  9,  1898,  $560;  Feb.  14,  1899,  $780.  How  much 
was  due  April  2,  1900? 


PARTIAL  PAYMENTS 


205 


Find  the  amounts  due : 


& 

Date  of  Debt 

Face 

Int. 

Payments 

Settled 

Aug.  15,  1896 

$1245 

4# 

Dec.  1,  1896,  $  208 
April  1,  1897,   315 
Nov.  15,  1897,   120 
July  6,  1898,   160 

Aug.  4,  1899 

3. 

May   6,  1898 

1790 

6# 

Aug.  8,  1898,   218 
Jan.  19,  1899,   350 
Dec.  14,  1899,   190 

July  12,  1900 

4. 

Oct.   4,  1897 

645 

6# 

Feb.  2,  1898,   175 
Oct.   8,  1898,   225 
Sept.  29,  1899,   130 

Oct.  16,  1900 

5. 

Jan.   6,  1896 

3255 

5# 

Oct.  12,  1896,   250 
May  4  1897,   380 
Feb.  26,  1898,  1650 

Dec.  7,  1898 

363.  When  a  payment  is  less  .than  the  interest  due  on  the 
debt,  the  payment  is  not  deducted  from  the  amount  due,  but  it 
is  added  to  the  next  payment,  and  the  sum  is  considered  as  one 
payment  bearing  the  date  of  the  latter  payment. 

EXAMPLE. — A  mortgage  for  $2500  was  given  Jan.  4,  1896. 
The  following  payments  were  made:  July  7,  1896,  $350;  Feb. 
15,  1897,  $50;  Oct.  4,  1897,  $540;  May  4,  1898,  $60;  Dec.  22, 
1898,  $425.  How  much  was  due  April  1,  1899? 

OPERATION 

Face  of  debt $2500.00 

Int.  to  first  payment 41.25 

Amt.  due  at  first  payment $2541.25 

First  payment 35000 

Amt.  due  after  first  payment $2191.25 

Int.  to  second  payment* 159.96 

Amt.  due  at  second  payment $2351.21 

Second  payment 590.00 

Amt.  due  after  second  payment $1761.21 

Int.  to  third  payment* 131.21 

Amt.  due  at  third  payment $1892.42 

Third  payment 485.00 

Amt.  due  after  third  payment $1407.42 

Int.  to  settlement 42.93 

Amt.  due  at  settlement $1450. 35 

*This  is  the  sum  of  two  payments  with  the  date  of  the  latter,  for 
the  former  was  less  than  the  interest  due.  The  pupil  can  generally 
tell  by  inspection  whether  the  interest  due  is  greater  than  the  payment 


Subtraction  of  Dates 

Year 

Month 

Day 

1899 

4 

1 

1898 

12 

22 

1898 

5 

4 

1897 

10 

4 

1897 

2 

15 

1896 

7 

7 

1896 

1 

4 

6 

3 

7 

8 

7 

19 

7 

0 

7 

18 

3 

9 

206 


MODERN    COMMERCIAL   ARITHMETIC 


PROBLEMS 


Find  the  amounts  due : 


1. 

Date 

Face 

Int. 

Payments 

Settled 

March  20,  1897 

$1540 

6# 

Sept.  14,  1897,  $  85 
June   6,  1898,   50 
Dec.   7,  1898,  320 
Feb.   3,  1899,  245 

Nov.  1,  1899 

2. 

Dec.  21,  1898 

2435 

4# 

May   3,  1899,  140 
Jan.   17,  1900,   60 
June   1,  1900,   75 
Sept.   4,  1900,  420 

Nov.  3,  1900 

3. 

Aug.   1,  1896 

630 

6# 

Oct.   8,  1896,  115 
Feb.   16,  1897,   50 
Jan.   1,  1898,   25 
Dec.  11,  1899,  325 

April  16,  1900 

I 

Nov.  22,  1897 

1182 

6# 

May   7,  1898,   25 
Sept.   3,  1898,   85 
March  21,  1899,  256 
Aug.   4,  1899,  120 

July  3,  1900 

5. 

Feb.   4,  1895 

2090 

Sfo 

Oct.   26,  1895,  235 
July  13,  1896,   90 
Jan.   12,  1897,  460 
May   4,  1897,  150 

Jan.  29,  1898 

6. 

Sept.   7,  1896 

875 

*% 

April  26,  1897,  145 
Oct.   6,  1897,  130 
May  18,  1898,  225 
Dec.  30,  1898,  160 

March  1,  1899 

7. 

May   3,  1898 

1470 

§% 

Nov.  29,  1898,  110 
Sept.  28,  1899,  160 
Jan.   8,  1900,  440 

Aug.  8,  1900 

8. 

July   2,  1896 

2100 

*% 

Dec.   1,  1896,  220 
Aug.   9,  1897,  165 
Feb.   4,  1898,  235 
Nov.  28,  1898,   50 

April  15,  1899 

9. 

June  19,  1897 

1360 

§% 

Nov.  10,  1897,  135 
March  11,  1898,  290 
Feb.   16,  1899,  325 
April  3,  1900,  165 

Sept.  21,  1900 

10. 

Jan.   4,  1898 

2900 

*% 

June  13,  1899,  180 
Aug.  16,  1899,   70 
Oct.   24,  1899,  390 
Sept.   6,  1900,  625 
Dec.  21,  1900,  750 

Jan.  10,  1901 

OF  THE 

UNIVERSITY 

OF 

INTEREST  207 


364.  TRUE  DISCOUNT 

MENTAL  PROBLEMS 

1.  What  will  $1  amount  to  in  1  yr.  at  6%?     In  2  yr.?     In 
3yr.? 

2.  What  will  $100  amount  to  in  1  yr.  at  6%?     In  2  yr.? 

8.  What  sum  now  will  amount  to  $106  in  1  yr.  at  6%?  To 
$112  in  2  yr.?  To  $118  in  3  yr.? 

4.  What  is  the  present  value  of  $106  due  in  1  yr.,  if  money 
is  worth  6%?     What  is  the  present  value  of  $112  due  in  2  yr.? 
Of  $118  due  in  3  yr.? 

5.  What  is  the  present  value  of  $212  due  in  1  yr.,  if  money 
is  worth  6%?     Of  $208  due  in  1  yr.,  if  money  is  worth  4%? 

6.  If  you  owe  $106  on  a  credit  of  1  yr.,  how  much  ought 
you  to  pay  if  you  pay  the  debt  now,  money  being  worth  6%? 

7.  If  you  owe  $115  on  3  yr.  credit,  how  much  should  you 
pay  now  to  cancel  the  debt,  money  being  worth  5%? 

8.  If  you  owe  $112  on  2  yr.  credit,  how  much  should  your 
creditor  allow  if  you  pay  the  debt  now,  money  being  worth  6  %  ? 

9.  If  you  owe  $210  on  1  yr.   credit,  how  much  discount 
should  you  be  allowed  if  you  pay  the  debt  now,  money  being 
worth  5%? 

10.  If  you  owe  now  $210,  which  is  to  be  paid  in  2  yr.,  with 
interest  at  5  %  ,  how  much  should  you  pay  to  cancel  the  debt 
now? 

365.  $100  in  cash  is  worth  more  than  $100  to  be  paid  in  1 
yr.,  without  interest.     It  is  worth  as  much  as  $100  to  be  paid 
in  1  yr.,  with  interest.     If  a  man  has  a  sum  of  money  due  him 
at  a  future  time  without  interest,  he  can  afford  to  allow  a  dis- 
count from  the  face  of  the  debt  if  it  is  paid  now. 

An  equitable  deduction  made  from  the  face  of  a  debt,  due 
at  a  future  time,  without  interest,  is  called  Time  Discount,  or 
True  Discount. 

366.  What  a  d§bt,  due  in  the  future,  without  interest,  is 
worth  now,  is  the  Present  Worth  of  the  debt.     The  present 


208  MODERN    COMMERCIAL   ARITHMETIC 

worth  of  a  debt  is  that  sum  which  put  at  interest  now  will 
amount  to  the  face  of  the  debt  when  it  falls  due. 

Face  of  debt  —  present  worth  =  discount 
Face  of  debt  —  discount  =  present  worth 

EXAMPLE. — I  owe  $2935.50  to  be  paid  in  6  mo.,  without 
interest.  What  is  the  present  worth  and  the  true  discount,  if 
money  is  worth  6  %  ? 

OPERATION 

$1  now  =  $1.03  due  in  6  mo. 
$2935.50  -f-    1.03  =  $2850,  present  worth 
$2935.50  -  $2850  =  $85.50,  true  discount 

EXPLANATION.— $1  now  =  $1.03  due  in  6  mo.  Each  $1.03  found  in 
$2935.50  is  equivalent  to  $1  due  now.  Therefore  $2935.50  -f-  1.03  =  the 
number  of  dollars  due  now. 

NOTES. — 1.  The  present  worth  of  an  interest  bearing  debt  is  the 
face  of  the  debt,  if  discounted  at  the  interest  bearing  rate. 

2.  When  an  interest  bearing  debt  is  discounted,  the  amount  of  the 
debt  when  it  becomes  due  should  be  taken  as  the  face  of  the  debt  to  be 
discounted. 

PROBLEMS 

1.    $840.00.  St.  Louis,  Mo.,  July  6,  1900. 

Eight  months  after  date  I  promise  to  pay  G.  O. 
Black,  or  order,  eight  hundred  forty  dollars,  for  value 
received.  WILLIAM  JOHNSON. 

How  much  was  the  above  note  worth  July  6,  if  money  was 
worth  6%? 

#.     $1250.00.  Charleston,  S.  C.,  Aug.  1,  1900. 

One  year  after  date  I  promise  to  pay  H.  A.  Wells, 
or  order,  twelve  hundred  fifty  dollars,  for  value 
received.  A.  D.  NOYSE. 

What  was  the  above  note  worth  Oct.  18,  1900,  money  being 
worth  6%? 

Find  the  present  worth  and  the  true  discount  of  the  fol- 
lowing : 

3.  $1217  on  90  da.  credit,  money  worth  4%. 

4.  $625.80  due  in  1  yr.  4  mo.  32  da.,  money  worth  6%. 


INTEREST  209 

5.  $3084  payable  in  7  mo.  29  da.,  money  worth  8%. 

6.  $215.25  payable  in  1  yr.  6  mo.  18  da.,  money  worth  6%. 

7.  $1028  payable  in  60  da.,  money  worth  7%. 

8.  $2135  payable  in  2  yr.  8  mo.,  money  worth  4£%. 

9.  $716  payable  in  3  yr.  3  mo.,  money  worth  6%. 

10.  $937  payable  in  1  yr.  4  mo.,  money  worth  6%. 

11.  What  sum  will  amount  to  $1438  in  2  yr.  7  mo.,  at  6%? 

12.  I  gave  my  note  for  $3625,  for  1  yr.,  with  4%  interest. 
If  the  note  is  discounted  at  6  % ,  what  should  I  pay  now? 

13.  On  Jan.  1,  1900,  I  agreed  to  pay  $1275  in  1  yr.  4  mo., 
with  interest  at  4%.     Four  months  later  the  debt  was  dis- 
counted at  6%.     What  did  I  pay? 

H.  Which  is  better  and  how  much,  to  buy  sheep  at  $8.50 
on  7  mo.  time,  or  to  pay  $8. 25  cash,  money  being  worth  6  %  ? 

15.  A  man  was  offered  a  house  for  $18500  cash,  or  $19400 
due  in  10  mo.     If  money  was  worth  6%,  which  was  the  better 
offer? 

16.  When  money  is  worth  4%,  what  cash  offer  is  equivalent 
to  an  offer  of  $2550  on  6  mo.  credit? 

17.  An  agent  bought  a  house  for  $1200.     He  kept  it  14 
mo.,  paid  $185  for  repairs,  and  sold  it  for  $1500,  on  9  mo. 
credit.     What  was  his  gain  or  loss,  if  money  was  worth  4%? 

18.  A    merchant    sold  $1475   worth   of  goods   on   8   mo, 
credit.     If  he  sold  the  goods  at  a  gain  of  20%,  what  was  his 
actual  gain  per  cent,  money  being  worth  6%? 

19.  Which  is  the  better  bargain  for  the  purchaser,  and  how 
much  better,  $1000  worth  of  goods  bought  on  8  mo.  time,  or 
5  %  off  for  cash,  money  being  worth  6  %  ? 

20.  Find  the  present  worth  of  a  debt  of  $6580,  $2000  of 
which  is  due  in  8  mo.,  $1500  in  14  mo.,  and  the  remainder  in 
1  yr.  8  mo.,  money  being  worth  6%. 

NOTE.— Find  the  present  worth  of  each  payment. 

'21.  George  is  17  yr.  old.  How  much  must  be  invested  for 
him,  at  5%  simple  interest,  that  he  may  have  $10000  of  prin- 
cipal and  interest  when  he  becomes  of  age? 

22.  I  bought  a  stock  of  goods  on  8  mo.  time.  After  hold- 
ing them  6  mo.,  I  sold  them  at  an  advance  of  25%,  giving  a 


210  MODERN    COMMERCIAL   ARITHMETIC 

credit  of  10  mo.  What  was  my  gain  per  cent,  money  being 
worth  6%? 

28.  A  man  agreed  to  pay  a  debt  of  $1200  in  6  equal  semi- 
annual payments,  with  simple  interest  at  4%  per  annum.  Two 
months  later  he  paid  the  present  worth  of  the  debt,  discounted 
at  6%  per  annum.  What  was  the  amount  of  the  discount? 

24.  On  a  bill  of  goods  for  $7850,  a  trade  discount  of  20%, 
15%,  and  10%  and  a  credit  of  6  mo.  is  allowed.  What  should 
be  the  total  discount  for  cash  payment,  money  being  worth  5%? 


BANKING  BUSINESS 

BANK   DISCOUNT 

367.  A  business  man  frequently  takes  notes  for  one,  two, 
or  three  months,  or  longer,  without  interest  or  with  interest. 
If  he  wishes  to  procure  the  money  on  a  note  before  it  becomes 
due,  he  may  present  it  to  a  bank,  which  will  purchase  it  from 
him.     The  amount  that  a  bank  deducts  from  the  face  of  the 
note  for  advancing  the  money  is  called  Bank  Discount. 

368.  For  discount  banks  take  the  legal  interest  on  the 
amount  due  at  maturity,  for  the  time  between  the  date  of  dis- 
counting and  the  date  when  the  note  becomes  due. 

369.  The  time  for  which  a  note  is  discounted  is  the  Term 
of  Discount. 

370.  The  amount  due  on  a  note  at  maturity  less  the  bank 
discount  is  the   Proceeds  of  the   note.      The  proceeds  of  a 
note  are  the  sum  received  by  its  owner  when  he  has  it  discounted 
at  a  bank, 

371.  In  discounting  a  note,  its  value,  for  discount  pur- 
poses, is  its  future  worth  (what  it  will  be  worth  when  it  falls 
due).     If  a  note  does  not  draw  interest,  its  future  worth  is  its 
face.     If  a  note  draws  interest,  its  future  worth  is  its  princi- 
pal plus  the  interest  to  maturity. 

372.  Difference  betiveen  True  and  Bank  Discount. — True 
discount  is  interest  on  the  present  worth  of  a  debt.     Bank  dis- 
count is  interest  on  the  future  worth  of  a  debt. 

MENTAL  PROBLEMS 

1.  What  is  the  bank  discount  on  a  note  for  $500,  if  the 
term  of  discount  is  2  mo.  and  the  interest  rate  for  discount 
is  6%?  What  are  the  proceeds? 

211 


212  MODERN    COMMERCIAL   ARITHMETIC 

2.  What  is  the  bank  discount  on  a  non-interest  bearing  note 
for  $200,  due  in  2  mo.,  money  being  worth  6%? 

3.  What  is  the  bank  discount  on  an  interest  bearing  note 
for  $200,  due  in  2  mo.,  money  being  worth  6%? 

4.  A  debt  of  $300,  without  interest,  is  due  in  2  mo.,  and 
money  is  worth  6%. 

What  is  the  future  worth  of  the  debt? 

What  is  the  present  worth  by  true  discount? 

What  is  the  interest  on  the  present  worth  for  2  mo.? 

What  is  the  sum  of  the  interest  on  the  present  worth  and 
the  present  worth? 

What  is  the  bank  discount? 

What  are  the  bank  proceeds? 

What  is  the  interest  on  the  proceeds  for  2  mo.?  On  the 
interest  on  the  interest  on  the  proceeds  for  2  mo.? 

What  is  the  sum  of  the  proceeds,  interest  on  the  proceeds, 
and  interest  on  the  interest  on  the  proceeds? 

Proceeds  +  int.  on  proceeds  +  int.  on  int.  on  proceeds  =  future 
worth. 

Present  worth  +  int.  on  present  worth  =  future  worth. 

373.  If  a  merchant  intends  to  have  a  note  discounted  at  a 
bank,  he  has  the  maker  make  the  note  payable  at  the  bank  with 
which  the  merchant  does  business.  Then  when  the  merchant 
wishes  to  have  the  note  discounted,  he  indorses  it  and  presents 
it  to  the  bank.  The  note  becomes  payable  to  the  bank,  and  the 
bank  pays  the  merchant  the  proceeds  of  the  note,  which  is  the 
future  worth  less  the  interest  on  the  future  worth  for  the  term 
of  discount. 

374*  A  note  made  payable  at  a  bank  is  called  a  Bank  Note, 
and  is  usually  in  this  form : 

^350.00.  Brooklyn,  N.  Y.,  Jan.  1,  1900. 

Two  months  after  date  I  promise  to  pay  to  the 
order  of  Richard  Roe  three  hundred  fifty  dollars,  at 
the  First  National  Bank,  Brooklyn,  N.  Y.  Value 
received  JOHN  DOE. 

Due  March  1. 


BANKING    BUSINESS  213 

EXAMPLE  1. — The  above  note  was  indorsed  in  blank  by 
Richard  Roe  and  presented  to  the  First  National  Bank  of 
Brooklyn,  Feb.  1,  1900.  What  were  the  term  of  discount,  the 
bank  discount,  and  the  proceeds,  money  being  worth  6%? 

OPERATION 

Term  of  disc.  =  28  da.,  time  from  Feb.  1  to  March  1 
Bank  disc.       =  $1.63,  int.  on  $350  for  28  da. 
Proceeds          =  $350  -  $1.63,  or  $348.37 

EXAMPLE  2. — 

$200.00.  Syracuse,  N.  Y.,  June  1,  1900. 

Ninety  days  after  date  I  promise  to  pay  to  the 
order  of  J.  L.  Johnson  two  hundred  dollars,  for  value 
received,  with  interest  at  6  per  cent,  at  the  State 
Bank,  Syracuse,  N.  Y.  LESTER  BROWN. 

Due  Aug-.  29. 

Tliis  note  was  discounted  by  the  bank  July  12.     Find  the  bank 
discount  and  the  proceeds. 

OPERATION 

Term  of  disc.  =  48  da.,  time  from  July  12  to  Aug.  29 
Future  worth  =  $203,  face  plus  interest  for  90  da. 
Bank  disc.       =  $1.62,  int.  on  $203  for  48  da. 

Proceeds          =  $203  -  $1.62  =  $201.38. 

PROBLEMS 
Find  the  discount  and  the  proceeds  of  the  following  notes: 

Rate  of 
Face  Date  Time          Interest          Discounted   Discount 

1.  $185        Jan.       2,  1900         4  mo.        4#         Jan.      18,  1900        6# 

2.  225        Feb.     21,  1900       90  da.         None    April     2,  1900        5% 
S.        436        Jan.     10,1900         3  mo.        5%        Feb.       1,1900        6# 

4.  250  April     2,  1900  6  mo.  8#  May       3,  1900  6% 

5.  712  July       6,  1900  30  da.  None  July       6,  1900  4% 

6.  456  March  15,  1900  2  mo.  None  March  28,  1900  6^ 

7.  575  June    12,  1900  60  da.  1%  July      2,  1900  1% 

8.  326  Feb.       9,  1900  90  da.  §%  Feb.     21,  1900  6^ 

9.  Find  the  discount  and  the  proceeds  of  the  following: 
$485.00.  Omaha,  Neb.,  Feb.  6,  1900. 

Three    months   after  date,    for  value  received,   I 
promise  to  pay  Thomas  Wentworth,  or  order,  four 
hundred  eighty-five  dollars,    with  interest  at  6  per 
cent,  at  the  First  National  Bank.          H.  R.  BECK. 
Discounted  Feb.  15,  at  6%. 


MODERX    COMMERCIAL    ARITHMETIC 


10.  1318.00.  Philadelphia,  Pa.,  Jan.  2,  1900. 

Ninety  days  after  date,  for  value  received,  1  prom- 
ise to  pay  to  the  order  of  C.  D.  Eaton  three  hundred 
eighteen  dollars,  at  the  Girard  Bank. 

HAROLD  SPENCER. 

Find  the  proceeds  if  discounted  Jan.  17,  at  6%. 

11.  §640.00.  Lexington,  Ky.,  April  4,  1900. 

Four  months  after  date",  for  value  received,  I 
promise  to  pay  to  the  order  of  James  Nelson  six  hun- 
dred forty  dollars,  with  interest  at  5  per  cent,  at  the 
Commercial  Bank.  L.  R.  WATSON. 

Find  the  proceeds  if  discounted  April  30,  at  6%. 

12.  $525.00.  Charleston,  S.  C.,  May  4,  1900. 

Six  months  after  date,  for  value  received,  I  promise 
to  pay  L.  C.  Westcott,  or  order,  five  hundred  twenty- 
five  dollars,  with  interest  at  6  per  cent,  at  the  Mer- 
chants' Bank.  R  A.  VANCE. 

Find  the  proceeds  if  discounted  June  12,  at  6%. 

Find  the  discount  and  the  proceeds  of  the  following  notes : 

Rate  of 
Discounted    Discount 

Feb.     1, 1900  6# 

April  30,  1900  §% 

June  25,  1900  5$ 

Aug.  28,  1900  8# 

Aug.    3,  1900  ±% 

April  28,  1900  6^ 

July  25,  1900  6^ 

June  18,  1900  §% 

Jan.   12,  1900  6# 

Feb.  24,  1900  6# 


Face 

Date 

Time 

Interest 

IS.  $1160 

Jan.      4,  1900 

4  mo. 

None 

U.       475 

April  17,  1900 

90  da. 

6# 

15.       329 

June  22,  1900 

30  da. 

None 

16.     1275 

Aug.    4,  1900 

3  mo. 

8# 

17.       738 

July  20,  1900 

90  da. 

None 

18.      426 

April   6,  1900 

60  da. 

None 

19.      375- 

June    7,  1900 

4  mo. 

4* 

20.       526 

March  5,  1900 

6  mo. 

6# 

21.      840 

Jan.    12,  1900 

30  da. 

None 

22.      237 

Feb.    20,  1900 

60  da. 

None 

BANK  DEPOSITS  AND  CHECKS 

375*  Savings  banks  receive  money  from  individuals  and 
pay  interest  on  such  deposits.  The  depositor  receives  a  bank 
book  in  which  the  sums  deposited  are  credited  to  him.  When 
he  draws  out  money,  the  amount  is  debited  to  him. 


BANKING    BUSINESS  215 

Commercial  banks  also  receive  deposits.  Some  commercial 
banks  pay  interest  on  deposits,  and  some  do  not.  Deposits  are 
often  made  for  safe-keeping. 

376.  When  a  depositor  in  a  commercial  bank  wishes  to 
draw  on  his  deposit  for  his  own  use,  he  writes  a  check,  of  which 
the  following  is  a  form : 

New  York,  Jan  2,  1900. 

FIRST  NATIONAL  BANK  OF  NEW  YORK. 
Pay  to  Self- 
One  Hundred  Eighty  Dollars.  $180.00. 

AMOS  WENTWORTH. 

If  Amos  Wentworth  wishes  to  pay  $180  from  his  deposit,  to 
J.  Higginson,  he  writes  a  check  as  follows: 

New  York,  Jan.  2,  1900. 

FIRST  NATIONAL  BANK  OF  NEW  YORK 
Pay  to  the  order  of  J.  Higginson — 
One  Hundred  Eighty  Dollars.  $180.00. 

AMOS  WENTWORTH. 

In  this  case  J.  Higginson  must  indorse  the  check. 

377.  The  one  who  signs  a  check  is  called  the  Drawer. 

378.  The  one  to  whom  the  check  is  made  payable  is  the 
Payee. 

379.  The  one    to  whom  the  check  is   addressed  is   the 
Drawee. 

380.  The  drawer  must  be  a  depositor.     It  sometimes  hap- 
pens that  a  depositor  of  good  financial  standing  draws  out  more 
than  he  has  deposited. 

The  payee  may  be  the  drawer,  bearer,  or  any  person  named 
in  the  check. 

381.  When  a  person  deposits  money  in  a  bank,  the  bank 
holds  the  money  subject  to  his  order  in  the  form  of  a  check. 

Assume  that  you  have  $500  deposited  in  a  bank,  and  wish 
to  draw  out  $100  for  yourself  and  wish  to  pay  Wm.  Springer 
$200.  Write  two  checks  that  will  accomplish  the  result. 

Write  a  check  so  that  only  James  Wells  can  draw  the 
money. 


216  MODERN    COMMERCIAL    ARITHMETIC 

383.  Many  banks  issue  Certificates  of  Deposit,  of  which 
the  following  is  a  form: 

No.  165.  CERTIFICATE  OF  DEPOSIT. 

FIRST   NATIONAL  BANK  OF  CLEVELAND. 

Cleveland,  Ohio,  Jan.  2,  1900. 

John  Doe  has  deposited  in  this  Bank  three  hundred  dollars, 
payable  to  his  order  on  the  return  of  this  Certificate  properly 
indorsed,  with  interest  at  3  per  cent. 

H.  WILSON,  Teller.  RICHARD  ROE,  Cashier. 

BANK  LOANS 

383.  A  depositor  may  borrow  money  from  a  bank  and  give 
his  note  for  the  sum  borrowed.     Usually  the  bank  requires  the 
borrower  to  deposit  some  security,  as  stocks,  bonds,  etc.,  or  to 
have  some  responsible  party  indorse  the  borrower's  note. 

Such  notes  are  called  Bank  Notes. 

384.  If  the  First  National  Bank  of  Detroit  is  willing  to 
loan  James  Wilson  $100  on  his  note,  the  form  might  be  as 
follows : 

$100.00.  Detroit,  Mich.,  Jan  2,  1900. 

Two  months  after  date  I  promise  to  pay  the  First 
National  Bank  of  Detroit,  Mich. ,  one  hundred  dollars. 
Value  received.  JAMES  WILSON. 

Due  March  2. 

385.  Bank  notes  are  usually  for  one,  two,  or  three  months, 
or  for  30,  60,  or  90  days.     They  do  not  draw  interest,  but 
interest  is  paid  in  advance  in  tbe  form  of  discount.     Thus,  on 
the  above  note  James  Wilson  would  receive  $100  -  $1  (discount 

for  2  mo.),  or  $99. 

PROBLEMS 

Find  the  net  amount  received  from  the  bank  as  proceeds  of 
each  of  the  following  notes : 


Face 

Time 

Rate  of 
Discount 

Face 

Rate  of 
Time        Discount 

1. 

$  340 

60 

da. 

5% 

7. 

$400 

30 

da. 

8% 

2. 

$  250 

3 

mo. 

6% 

8. 

$360 

2 

mo. 

4% 

8. 

$  475 

1 

mo. 

8% 

9. 

$520 

90 

da. 

6% 

4. 

$  600 

90 

da. 

4% 

10. 

$175 

1 

mo. 

7% 

5. 

$  850 

30 

da. 

6% 

11. 

$230 

'  60 

da. 

6% 

6. 

$1200 

2 

mo. 

6% 

12. 

$150 

90 

da. 

8% 

BANKING   BUSINESS  217 

386.  If  the  First  National  Bank  of  Detroit  is  willing  to 
loan  James  Wilson  $100  on  a  note  indorsed  by  Wm.  Sully,  the 
form  of  the  note  might  be  as  follows: 

$100.00.  Detroit,  Mich.,  Jan.  2,  1900. 

Two  months  after  date  I  promise  to  pay  Wm.  Sully, 
or  order,  one  hundred  dollars,  at  the  First  National  Bank 
of  Detroit,  Mich.  Value  received, 

Due  March  2.  JAMES  WILSON. 

Wm.  Sully  indorses  the  note,  thus  making  it  payable  to  the 
bank,  and  also  making  himself  responsible  for  its  payment  in 
case  James  Wilson  fails  to  pay  it.  Wilson  can  secure  $99 
($100  -  $1  discount)  on  the  note.  Sully  indorses  the  note  to 
accommodate  Wilson,  and  he  is  called  an  accommodation 
indorser. 

387.  Such  notes,  if  not  paid  when  due,  draw  interest  from 
the  day  of  maturity  to  the  day  of  payment. 

388.  If   an  indorsed  note  is  not  paid  at   maturity,  the 
bank  immediately  sends  the  indorser  a  notice  of  protest. 

PROBLEMS 

1.  You  wish  to  borrow  $200  from  a  bank  that  will  accept 
your  note  if  indorsed  by  Lewis  Ross.     Write  the  note  for  three 
months.     If  discounted  at  6%,  what  would  be  the  net  amount 
received? 

2.  On  May  1,  1900,  E.  H.  Westcott  borrowed  $350  from  the 
Third  National  Bank  of  Cleveland,   Ohio,  for  3  mo.,  on  his 
note  indorsed  by  J.  C.  Stone.      Write  and  indorse  the  note. 
Find  the  proceeds  if  discounted  at  5%. 

3.  Wm.  Walton  borrowed  $350  from  the  Citizens'  Bank  of 
Boston,   Mass.,   on  a  2  mo.   note,   dated  June  4,   1900,  and 
indorsed  by  E.  H.  Jones.     Write  and  indorse  the  note.     Find 
the  amount  received  by  Walton  if  the  discount  is  6%.     If  he 
immediately  put  this  sum  at  interest  at  6%,  how  much  would 
he  lack  of  having  enough  to  pay  the  note  at  its  maturity?     If 
Walton  did  not  pay  the  note,  and  the  indorser  paid  it  Sept.  12, 
1900,  what  sum  did  he  pay,  interest  at  6%? 


218  MODERN    COMMERCIAL   ARITHMETIC 

COLLATERAL   NOTES 

389.  A  Collateral  Note  is  one  whose  payment  is  secured  by 
making  a  deposit  of  personal  property. 

FORM   OF    NOTE 

$25.00.  Buffalo,  N.  Y.,  July  8,  1902. 

Two  months  after  date,  for  value  received,  I  prom- 
ise to  pay  H.  B.  Swan,  or  order,  twenty-five  dollars, 
with  interest  at  6  per  cent.  As  security  for  the  pay- 
ment of  the  same  I  hare  deposited  herewith  a  Smith- 
Premier  typewriter,  No.  75863,  with  permission  to  sell 
the  same,  if  the  note  and  interest  thereon  are  not  paid 
at  maturity.  WALTER  C.  CLARK. 

RECEIPT   FOR   COLLATERAL 

Buffalo,  N.  Y.,  JulyS,  1902. 

Received  from  Walter  C.  Clark  a  Smith-Premier 
typewriter,  No.  75863,  to  secure  the  payment  of  a  note 
for  twenty -five  dollars,  given  this  day  by  said  Walter 
C.  Clark  to  me.  H.  B.  SWAN. 

390.  Life  insurance  policies,  stock  certificates,  notes,  mort- 
gages, etc.,  may  also  be  assigned,  or  transferred  to  secure  the 
payment  of  notes. 

PROBLEMS 

1.  $120.00.  Chicago,  111.,  July  2,  1902. 

Four  months  from  date,  for  value  received,  I  prom- 
ise to  pay  F.  E.  Welsh,  or  order,  one  hundred  twenty 
dollars,  with  interest  at  6  per  cent.  To  secure  the 
payment  of  this  note  I  deposit  herewith  a  diamond 
ring  marked  H.  K.  and  bought  of  Wilson  Bros.,  this 
city.  HAROLD  KNOX. 

What  was  due  on  the  note  Oct.  1,  1902? 

2.  On  July  22,  1902,  A.  L.  Ross  gave  an  interest  bearing 
note  for  $265   for  2  mo.  to  J.   A.   Briggs,  and   deposited  as 
security  for  its  payment  a  box  of  jewelry  with  permission  to 
sell  the  same  if  the  note  was  not  paid  at  maturity.     The  note 
was  not  paid  when  due,  .and  the  jewelry  was  sold  Oct.  15  for 
$340.     How  much  money  should  Briggs  pay  Eoss? 


BANKING   BUSINESS  219 

8.  A  gave  B  a  9-mo.  note  for  $375,  interest  at  6%,  and 
assigned  a  life  insurance  policy  as  security  for  payment.  What 
was  the  total  amount  due  B  4  mo.  after  the  note  became  due? 

4.  C  assigned  a  stock  certificate  to  D  bo  secure  the  payment 
of  a  loan  of  $225  made  May  1,  1902.     What  amount  did  C  pay 
on  Aug.  20,  1902,  to  redeem  his  stock  certificate? 

5.  On  June  3,  1902,  K.  H.  Empie  assigned  a  chattel  mort- 
gage to  C.  D.  Klein  to  secure  the  payment  of  a  loan  of  $130. 
What  amount  was  due  Klein  on  Aug.  27,  1902? 

DOMESTIC  EXCHANGE 

391.  A  keeps  a  meat  market  and  owes  B  for  cattle.     C 
works  for  B  by  the  month.     B  has  no  money  to  pay  C  until 
the  end  of  8  mo.     C  wishes  to  trade  at  the  market,  and  asks  B 
for  money.     B  writes  the  following  order : 

Avon,  N.  Y.,  April  4,  1900. 
Mr.   A:— 

Please  pay  to  C  forty  dollars  in  meats,  and  charge 
to  my  account.  B. 

If  A  accepts  the  order  C  can  trade  at  the  market,  and  A  will  also 
be  paying  $40  on  his  debt  to  C,  but  there  will  be  no  money  used. 

392.  A  owes  B  $100.     B  owes  C  $100.     C  owes  A  $100. 
How  do  these  men  stand  financially  after  the  following  order 

is  delivered?     "Mr.  C  :  Please  pay  to  B  $100.— A." 

Or  after  this  order?     "Mr.  A:    Please  pay  to  C  $100.— B." 
Or  after  this  order?     "Mr.  B:    Please  pay  to  A  $100.— C." 

393.  If  A  in  Boston  owes  B  in  St.  Louis  $100,  he  may 
pay  the  debt  in  one  of  five  ways  without  sending  money. 

(a)  A  may  go  to  the  postoffice  in  Boston  and  buy  a  Postal 
Money  Order  for  $100.  He  would  fill  out  an  application  blank 
for  a  money  order,  in  which  he  would  state  the  sum  to  be  paid, 
to  whom  to  be  paid,  and  where  to  be  paid.  The  postmaster 
would  then  give  A  an  order,  which  would  direct  the  postmaster 
at  St.  Louis  to  pay  $100  to  the  person  to  be  named  by  the 
postmaster  of  Boston  in  a  letter  of  advice.  A  would  send  the 
order  to  B.  The  Boston  postmaster  would  tell  the  St.  Louis 
postmaster  in  a  "letter  of  advice"  to  pay  the  order  to  B.  BT 


220  MODERN    COMMERCIAL   ARITHMETIC 

upon  receiving  the  order,  would  take  it  to  the  postoffice  and 
get  $100.  The  postmaster  at  Boston  would  charge  A  $100.30 
for  the  order. 

At  the  present  time  money  orders  are  issued,  for  any  amount 
up  to  $100,  at  the  following  rates : 

$  2.50  or  less 3^               §30.00  to  $  40.00 15? 

2.50  to  $  5.00 5?                 40.00  to      50.00 IS? 

5.00  to  10.00 8?  50. 00  to  60.00 20? 

10. 00  to  20.00 W  60.00  to  75.00 25^ 

20.00  to  30.00 12?  75.00  to  100.00 30J* 

(b)  A  may  buy  an  Express  Money  Order  from  an  express 
company  in  Boston.     Express  money  orders  are  similar  to  pos- 
tal money  orders.      The  agents  of  the  company  at  different 
offices  of  the  company  issue  orders  on  one  another  as  do  the 
postmasters.     The  rates  for  express  money  orders  are  the  same 
as  for  postal  money  orders. 

(c)  A  may  go  to  a  telegraph  office  in  Boston  and  buy  a  Tele- 
graphic Money  Order.     The  agent  of  the  telegraph  company  at 
Boston  would  telegraph  to  the  company's  agent  at  St.  Louis  to 
pay  B  $100.     The  rates  for  telegraphic  money  orders  are  higher 
than  the  rates  for  the  other  orders  mentioned,  but  the  exchange 
is  made  much  more  quickly. 

(d)  A  may  buy  from  a  Boston  bank  a  Draft  made  payable 
to  B.     A  would  pay  the  Boston  bank  $100  plus  the  charge  for 
"exchange."     The  Boston  bank  would  write  an  order  for  some 
bank  with  which  it  has  money  deposited,  to  pay  B  $100.     This 
order  would  be  a  Check  of  the  Boston  bank,  but  when  a  bank 
draws  its  check  the  paper  is  called  a  draft.     The  Boston  bank 
would  give  the  order,  or  draft,  to  A,  who  would  send  it  to  B. 
B  could  take  it  to  a  bank  and  have  it  cashed.     The  form  of 
the  draft  might  be : 

FIRST  NATIONAL  BANK  OF  BOSTON. 

Boston,  Mass.,  Jan.  2,  1900. 

Pay  to  the  order  of  B 

One  Hundred  Dollars.  $100.00. 

T.  A.  WILSON,  Cashier. 
To  the  Mercantile  National  Bank, 
New  York  City. 


BANKING   BUSINESS 

The  draft  might  be  made  payable  to  A,  who  would  then 
indorse  it  in  favor  of  B. 

Drafts  and  checks  are  much  alike  in  form,  but  a  check  is 
drawn  by  a  party,  not  a  bank,  on  a  bank,  while  a  draft  is  drawn 
by  a  bank  or  banker  on  another  bank. 

(e)  If  A  has  money  deposited  in  a  Boston  bank,  he  may 
send  B  a  check  like  the  following : 

Boston,  Mass.,  Jan.  2,  1900. 
First  National  Bank  of  Boston,  Mass.  :— 

Pay  to  the  order  of  B 

One  Hundred  Dollars.  $100.00. 

(Signed)  A. 

If  B  has  a  bank  account  with  a  St.  Louis  bank,  he  may 
indorse  the  check  and  deposit  it  with  the  bank,  which  will 
probably  collect  it  for  him  without  charge.  When  B  indorses 
the  check  he  becomes  responsible  for  its  payment,  and  since  he 
has  a  deposit  in  the  bank,  the  bank  is  safe  in  accepting  the 
check. 

If  B  has  no  bank  account,  he  may  indorse  the  check  and 
present  it  to  a  bank.  The  bank  will  pay  the  check  after 
ascertaining  that  it  is  good. 

If  B  has  no  bank  account,  he  may  indorse  the  check  and 
send  it  direct  to  the  Boston  bank,  which  will  send  him  a  draft 
for  $100  less  a  charge  for  exchange.  This  draft  B  may  have 
cashed  by  a  bank. 


Cost  of  Drafts 

394.  Banks  sell  drafts,  or,  as  it  is  termed,  sell  "exchange." 
The  cost  of  a  draft  is  the  face  of  the  draft  plus  the  charge 

for  exchange. 

395.  New  York  or  Chicago  exchange,  drafts  on  New  York 
or  Chicago  banks,  usually  sell  at  a  premium  of  about  .1%.     A 
draft  for  $500  would  probably  cost  $500.50.     On  small  drafts  a 
definite  charge,  as  10$  or  15^,  may  be  made. 


222  MODERN   COMMERCIAL   ARITHMETIC 

PROBLEMS 

1.  Find  the  cost  of  a  draft  for  $850  bought  in  Buffalo  and 
drawn  on  a  New  York  bank,  if  the  Buffalo  bank  charges  a 
premium  of  |%  as  exchange. 

2.  What  will  be  the  cost  of  a  draft  on  Chicago  for  $1280, 
when  exchange  is  at  a  premium  of  J%? 

3.  A  merchant  of  Omaha  owes  a  wholesale  house  in  Mil- 
waukee $3800.     He  buys  of  his  banker  a  NQW  York  draft,  at  a 
cost  of  80  per  $100.     How  much  does  the  draft  cost? 

4.  Find  the  cost  of  a  draft  for  $1570  on  a  Chicago  bank, 
the  rate  of  exchange  being  .1%  premium? 

5.  Find  the  cost  of  a  Boston  draft  for  $9700,  at  the  rate  of 
100  per  $100. 

6.  An  agent  in  New  Orleans,  wishing  to  pay  his  principal 
in  New  York  $3265,  bought  a  New  York  draft  at-J-%  discount. 
What  did  the  draft  cost  him? 

7.  When  exchange  is  at  \°J0  premium,  what  will  a  draft  for 
$1  cost?     What  will  be  the  face  of  a  draft  that  $5.01  will  buy? 
What  will  be  the  face  of  a  draft  that  $851.70  will  buy? 

8.  An  agent  has  $2500  of  his  employer's  money  which  he  is 
to  remit  at  the  expense  of  the  employer.     What  will  be  the  face 
of  the  draft,  if  exchange  is  £%  discount? 

9.  What  will  be  the  cost  of  a  draft  for  $2635,  at  120  per 
$1000? 

10.  A  principal  directs  his  agent  to  send  him  the  money  he 
has  on  hand,  deducting  charges  for  the  draft.     If  the  agent  has 
$4500  of  his  employer's  money,  and  exchange  is  at  £%  premium, 
what  will  be  the  face  of  the  draft? 


The  Clearing  House 

396.  Each  large  city  is  a  money  center.  The  banks  in  the 
villages  and  smaller  cities  deposit  money  with,  remit  drafts  pay- 
able to,  and  sell  drafts  drawn  upon  the  banks  in  the  money 
centers.  In  New  York  State  money  is  usually  sent  from  one 
village  to  another  by  a  draft  drawn  on  a  New  York  bank. 


BAJSTKIKG   BUSINESS  223 

A  man  in  Livonia  wishes  to  send  $100  to  a  man  in  Koches- 
ter.  He  pays  the  Bank  of  Livonia  $100.50  for  a  draft  for  $100 
on  the  Chemical  Bank  of  New  York.  The  draft  is  sent  to 
Rochester  and  is  cashed  by  a  bank,  which  sends  the  draft  to 
the  Manhattan  Bank  of  New  York  and  is  credited  with  a 
deposit  of  $100. 

A  man  in  Dundee  wishes  to  send  $100  to  a  man  in  Livonia. 
He  pays  the  Dundee  National  Bank  $100.50  for  a  $100  draft 
on  the  Manhattan  Bank  of  New  York,  and  sends  the  draft  to 
Livonia.  The  Liviona  man  takes  the  draft  to  the  Bank  of 
Livonia,  which  cashes  the  draft  and  then  sends  it  to  the  Chem- 
ical Bank  of  New  York  to  pay  for  the  draft  which  the  Bank  of 
Livonia  first  drew  on  the  Chemical  Bank. 

The  Chemical  Bank  now  has  a  draft  for  $100  on  the  Man- 
hattan Bank,  and  the  Manhattan  Bank  has  a  draft  for  $100  on 
the  Chemical  Bank.  These  drafts  are  sent  to  the  Clearing 
House,  where  they  cancel  each  other. 

The  New  York  banks  send  agents  to  the  clearing  house  to 
exchange  the  drafts  held  by  each  on  the  others.  If  one  bank 
owes  all  the  others  $50000,  after  the  drafts  are  cancelled,  it 
pays  that  sum  to  the  clearing  house.  If  several  banks  owe  one 
bank  $50000,  the  clearing  house  pays  the  bank  that  sum.  The 
clearing  house  settles  the  accounts  between  the  various  banks. 
It  receives  from  the  debtor  banks  and  pays  to  the  creditor  banks. 
The  amount  of  money  exchanged  is  small  in  proportion  to  the 
value  of  the  drafts  exchanged.  The  "clearings"  (cancella- 
tions) at  the  New  York  clearing  house  for  1899  were  $57,368,- 
230,771,  and  the  balances  paid  in  money  were  $3,085,971,370. 

Each  of  the  great  American  cities  has  a  clearing  house,  but 
the  one  at  New  York  does  more  business  than  all  the  others 
combined. 

Fluctuation  of  Exchange 

397.  On  small  sums  the  rate  of  exchange  is  usually  at  a 
uniform  premium.  This  premium  is  to  pay  the  banks  for  their 
trouble.  Banks  usually  buy  New  York  and  Chicago  drafts  at 
par,  that  is,  the  banks  make  no  charge  for  collecting  the  drafts. 


224  MODERN    COMMERCIAL   ARITHMETIC 

398.  The  rate  of  exchange  on  large  sums  varies  in  the  differ- 
ent cities".      If  Denver  banks  owe  New  York  banks  large  sums, 
they  would  be  obliged  to  send  the  money  to  New  York,  which 
would  cause  delay  and  expense.     If  then  a  man  in  Denver 
wishes  to  buy  a  draft  on  New  York,  he  would  have  to  pay  more 
than  the  usual  rate  of  exchange,  for  the  Denver  banks  would 
then  have  to  send  more  money  to  New  York.     But  if  a  man  in 
New  York  wishes  to  buy  a  draft  on  Denver,  he  might  get  it  at 
a  discount,  for  then  the  New  York  banks  would  procure  a  portion 
of  their  money  from  Denver  immediately.     Thus  on  large  drafts 
between  distant  cities  the  rate  of  exchange  varies,  or  fluctuates. 

PROBLEMS 
Find  the  cost  of  each  of  the  following  drafts : 

Face  Rate  of  Exchange  Face  Rate  of  Exchange 

1.  $  2300         |%  premium  6.  $1684        -j-%  premium 

2.  $18250        -J%  discount  7.  $3790        \%  discount 
8.  $  6580         At  par                            8.  $1260         At  par 

4.  $     750.90   £%  premium  9.  $  538        .1%  discount 

5.  $  1585        £%  premium  10.  $2520         100  per  $100 

Commercial  Drafts 

399.  The  check  of  one  bank  on  another  to  effect  exchange 
is  called  a  Bank  Draft.     The  order  or  draft  of  one  individual 
or  firm  on  another,  asking  payment  of  a  debt  through  the 
agency  of  a  bank,  is  called  a  Commercial  Draft.     A  commer- 
cial draft  is  made  payable  at  a  certain  bank,  and  the  bank 
becomes  the  means  by  which  one  party  collects  from  another. 

400.  A  draft  may  be  made  payable  at  sight,  or  when  pre- 
sented for  payment.     Such  a  draft  is  called  a  Sight  Draft. 

SIGHT   COMMERCIAL   DRAFT 

Detroit,  Mich. ,  Jan.  2,  1900. 
At  sight,  pay  to  the  order  of  the  First  National 

Bank  of  Detroit 

Eighty-Five  Dollars.  $85.00. 

To  A.  B.  Wade,  E.  E.  LAMSON. 

Lansing,  Mich. 


BANKING   BUSINESS  225 

Wade  owed  Lamson  $85,  and  this  is  the  means  that  Lamson 
took  to  procure  payment.  Wade  paid  the  bank  $85,  and  the 
bank  paid  Lamson  $85  less  £%  discount  for  collecting. 

4O1.  A  draft  may  be  made  payable  a  certain  number  of  days 
after  sight,  or  after  date.  Such  a  draft  is  called  a  Time  Draft. 

TIME    COMMEKCIAL   DRAFT 

St.  Louis,  Mo.,  Jan.  2,  1900. 
Thirty  days  after  date  pay  to  the  order  of  the  Third 

National  Bank,  St.  Louis, 

One  Hundred  Fifty  Dollars.  $150.00. 

To  M.  D.  Clark,  R.  A.  WALL. 

Kansas  City,  Mo. 

Clark  owed  Wall  $150,  due  in  30  da.,  and  Wall  asked  pay- 
ment by  means  of  this  draft.  He  presented  the  draft  to  the 
bank  and  asked  to  have  it  discounted.  The  bank  sent  the 
draft  to  Clark,  who  "accepted"  it — agreed  to  pay  it  on  matur- 
ity. Clark  wrote  across  the  face  of  the  draft:  "Accepted, 
Jan.  3,  1900. — M.  D.  Clark,"  and  returned  the  draft  to  the 
bank.  The  bank  paid  Wall  .$150  less  the  bank  discount  on 
$150  for  30  days,  and  an  additional  discount  of  \%  for  collecting. 

If  the  drawer  of  a  commercial  draft  indorses  it  and  is  a 
responsible  party,  the  bank  will  pay  him  the  proceeds  of  the 
draft  (the  face  less  the  discount  for  time  and  for  collecting) 
without  waiting  for  the  drawee  to  pay  or  accept  the  draft.  If 
the  drawee  should  refuse  to  accept  and  pay  the  draft,  the 
drawer  by  his  indorsement  becomes  responsible  for  payment. 
A  draft  that  is  not  accepted  by  the  drawee  when  duly  pre- 
sented is  said  to  be  "dishonored." 

In  States  that  allow  grace,  grace  is  allowed  on  time  drafts. 

PROBLEMS 
Find  the  proceeds  of  the  following  drafts : 

1.  Albany,  N.  Y.,  July  6,  1900. 

At  sight  pay  to  the  order  of  the  First  National 
Bank,  Albany,  two  hundred  dollars. 

To  H.  W.  Reed.  JAMES  KIMM. 

The  bank  discounted  the  draft  at 


226  MODERN    COMMERCIAL   ARITHMETIC 

&  New  York  City,  Aug.  14,  1900. 

Sixty  days  after  sight  pay  to  the  order  of  the  Man- 
hattan National  Bank  of  New  York  one  hundred 
eighty  dollars. 

To  J.  A.  Weed,  .   L  M'  RCWE- 

New  York. 

The  bank  immediately  cashed  the  draft,  discounting  it  at  6% 
for  the  time  and  £%  for  collecting. 

$.  Boston,  Mass.,  Sept.  17,  1900. 

Thirty  days  after  date  pay  to  the  order  of  the 
Chemical  National  Bank,  Boston,  one  hundred  seventy- 
five  dollars,  and  charge  to  my  account. 

To  James  Elliot,  H.  W.  LONGWOOD. 

Lynn,  Mass. 

The  bank    advanced    the  money,  taking  out  time  discount, 
money  being  worth  6%. 

4.  A  Chicago  broker  bought  a  60-da.  commercial  draft  for 
$1800  on  a  New  York  company,  at  -J-%   discount.     Find  the 
cost  of  the  draft,  money  being  worth  6%. 

5.  Find  the  face  of  the  90-da.  commercial  draft  that  can  be 
bought  for  $825,  premium  -J-%,  interest  6%. 

EXPLANATION. — A  draft  for  $1  will  cost  II  +  $.0025  premium 
—$.015  interest,  or  1.9875.  If  1.9875  will  buy  a  draft  for  $1,  $825  will 
buy  a  draft  whose  face  is  as  many  dollars  as  $.9875  is  contained  times 
in  $825  or  $833.44. 

6.  Barr  and  Creelman  drew  a  60-da.  draft  on  the  Wilson 
Mfg.   Co.,  for  $2360,  and  sold  the  draft  to  the  Merchants' 
Bank,  at  £%   discount,  and  interest  at  6%.     What  were  the 
proceeds? 

7.  A  $580  sight  draft  was  sold  at  a  premium  of   1%.     Find 
the  proceeds. 

8.  A  Denver  broker  drew  a  60-da.  draft  on  a  Chicago  firm 
for  $2400.     Twenty  days  after  date  he  sold  the  draft  at  a  dis- 
count of  \  % ,  interest  at  6  % .     What  did  he  receive  for  the  draft? 


BANKING   BUSINESS  227 

FOREIGN  EXCHANGE 

402.  Foreign  Exchange  is  that  in  which  drafts  drawn  in 
one  country  are  payable  in  another.     It  differs  from  domestic 
exchange  in  the  currency  used  and  in  the  manner  of  quoting 
the  rate  of  exchange. 

403.  In    foreign    exchange    drafts    are    called    Bills    of 
Exchange. 

404.  The  rate  of  exchange  on  Great  Britain  is  quoted  by 
giving  the  value  of  1  sov.  in  dollars  and  cents.     Thus,  when 
exchange  on  London  is  quoted  4.87,  a  draft  for  1  sov.  will  cost 
$4.87. 

405.  Exchange  on  France  is  usually  quoted  by  giving  the 
value  of  $1  in  francs.     The  quotation  5.15  means  that  $1  is 
worth  5.15  francs.     Sometimes  exchange  is  quoted  by  giving 
the  value  of  1  franc  in  cents.     The  quotation  19.6  means  that 
1  franc  is  worth  19.6^. 

406.  In  Germany,  the  exchange  quotation  96  means  that  4 
marks  are  worth  96^.     The  quotation  24  means  that  1  mark  is 
worth  24^. 

407.  The  monetary  unit  of  Mexico  is  the  dollar.      The 
gold  dollar,  which  contains  nearly  the  same  amount  of  pure 
gold  as  onr  dollar,  is  worth  $.983  in  TJ.  S.  money;   and  the 
silver  dollar,  which  contains  nearly  the  same  amount  of  pure 
silver  as  our  silver  dollar,  is  worth  from  44^  to  49^  in  TJ.  S. 
money,  according  to  the  fluctuation  in  the  price  of  silver  as 
compared  with  gold. 

408.  The  gold  in  a  sovereign  is  worth  $4.8665  in  Ameri- 
can coined  gold.     The  quotation  4.8665  is,  therefore,  at  par. 
It  is  the  par  of  exchange.     The  par  of  exchange  on  France  is 
5.18J,  or  19.3,  whichever  way  the  quotation  is  made.     The  par 
of  exchange  on  Germany  is  95.2,  or  23.8. 

409.  The  Commercial  Rate  of  Exchange  may  be  at  par, 
above  par,  or  below  par.     It  is  the  market  value  in  one  country 
of  drafts  on  another. 

410.  Bills  of  exchange  were  formerly  drawn  in  triplicate, 
that  is,  three  bills  were  drawn  of  the  same  tenor  and  date,  one 


228  MODERN   COMMERCIAL   ARITHMETIC 

of  which  being  paid  the  others  became  void.  At  present  many 
bills  are  drawn  in  duplicate,  and  in  many  cases  only  a  single 
bill  is  drawn.  The  object  of  sending  two  or  three  bills  by 
different  routes  or  at  different  times  is  to  make  sure  that  one 
copy  will  reach  its  destination. 

PROBLEMS 

1.  What  will  be  the  cost  in  New  York  of  a  draft  on  London 
for  420  sov.  14s.,  exchange  at  4.86? 

2.  When    exchange    on  Liverpool,  England,  is  quoted  at 
4.86|,  what  is  the  face  of  a  draft  that  $1285  will  buy? 

3.  What  will  be  the  cost  of  a  bill  of  exchange  on  Berlin  for 
2540  marks,  exchange  at  95^-? 

4.  Find  the  cost  of  a  bill  of  exchange  drawn  on  Paris  for 
35800  francs,  exchange  at  5.16. 

5.  What  will  be  the  cost  in  Paris  of  a  bill  of   exchange 
drawn  on  New  York  for  $875,  exchange  at  5.17? 

6.  A  man  owes  a  London  merchant  $4560.     What  is  the 
face  of  the  draft  he  should  send,  exchange  at  4.86J? 

7.  A  man  in  New  York  owes  $3480  in  U.  S.  money  to  a 
dealer  in  Mexico.      If  exchange  on  Mexico  is  %%   premium, 
what  will  be  the  cost  of  a  draft  to  pay  the  debt? 

8.  A  speculator  in  Chicago  wishes  to  buy  $10000  worth  of 
Mexican  stock,  payable  in  silver.     What  must  be  the  face  of 
the  draft  if  a  Mexican  dollar  is  worth  49^  in  U.  S.  money? 
What  will  the  draft  cost  if  exchange  is  at  f  %  premium? 

9.  I  wish  to  invest  $10000  in  II.  S.  money  in  Mexican  silver 
bonds.     How  many  dollars'  worth  of  the  bonds  can  I  buy  if 
exchange  is  £  %  premium  and  the  par  of  exchange  is  49? 

10.  A  merchant  in  Mexico  owes  a  dealer  in  New  Orleans 
$18950  in  U.  S.  money.     How  many  Mexican  silver  dollars  will 
be  required  to  pay  the  debt,  exchange  at  •§•  %  discount  and  the 
par  of  exchange  at  49? 


ACCOUNTS  AND  BILLS 

411.  A  owes  B  $100.  To  A  this  item  is  a  debt,  to  B  it  is 
a  credit. 

4d2.  That  which  one  owes  another  is  a  Debt.  It  is  a  debt 
to  the  one  owing  it  and  a  credit  to  the  one  to  whom  it  is  owed. 

413.  That  which  one  has  paid  to  another  is  a  Credit.     It 
is  a  credit  to  the  one  who  has  paid  it,  and  a  debt  to  the  one 
who  has  received  it. 

What  is  bought  or  received  is  a  debt,  or  debit. 
What  is  sold  or  paid  is  a  credit. 

A  person  is  debited  to  what  he  receives,  and  credited  ly  what 
he  parts  with. 

414.  A  record  of  one  or  more  business  transactions  by  two 
individuals  or  firms  showing  the  proper  debits  and  credits  is  an 
Account. 

Thus,  a  merchant  keeps  an  account  with  each  person  deal- 
ing with  him.  He  heads  a  page  of  his  ledger  with  the  name 
of  a  customer.  In  a  column  headed  "Dr."  (debtor)  he  puts 
the  values  of  what  the  customer  receives.  In  a  column  headed 
"Cr."  (creditor)  he  puts  the  sums  that  the  creditor  pays. 

415.  The  difference  between  the  amount  of  the  debits  and 
credits  of  an  account  is  called  the  Balance  of  the  Account. 

If  the  balance  is  on  the  debtor  side  of  the  account,  it  shows 
that  the  customer  has  received  more  than  he  has  paid  for.  It 
shows  how  much  more  he  should  still  pay.  It  shows  how  much 
more  must  be  added  to  the  credit  side  of  the  account  to  bal- 
ance the  account. 

If  the  balance  is  on  the  credit  side  of  the  account,  it  shows 
that  the  customer  has  paid  for  more  than  he  has  received.  It 
shows  how  much  must  be  added  to  the  debit  side  of  the 
account  to  balance  the  account. 

416.  The   following  account   is  taken  from  the  account 
book  of  John  Doe: 

229 


230 


MODERN    COMMERCIAL   ARITHMETIC 


DR.  (has  received). 


WM.  SMITH. 


CR.  (has  paid). 


1900 

1900 

Jan. 

2 

To  lumber, 

$14.00 

Jan. 

3 

By  cash, 

§12.50 

4 

To  flour, 

7.80 

5 

By  labor, 

3.75 

5 

To  feed, 

6.20 

6 

By  balance, 

11.75 

$28.00 

12800 

It  is  found  that  the  Dr.  side  is  $11.75  greater  than  the  Or. 
side,  and  that  $11.75  must  be  added  to  the  Cr.  side  to  balance 
the  account.  This  shows  that  Wm.  Smith  should  pay  John 
Doe  $11.75. 

BILLS 

417.  A  detailed  statement  of  goods  sold  or  of  services  ren- 
dered is  called  a  Bill.     A  bill  of  goods  is  also  called  an  Invoice. 

418.  The  following  abbreviations  and  terms  are  frequently 
used: 

account 

agent 

amount 

balance 

bought 

charged 

Company 

commission 

collect  on  delivery 

consignment 


acct. 

agt. 

ami. 

ML 

bot. 

cJigd. 

Co. 

com. 

G.  0.  D. 

con. 

dft. 

disc. 

'exch. 

frt. 

guar. 
i.  e. 


Pp.,  or  pp.  pages 


mem. 
Messrs. 
N.  B. 
net 
No. 
P.,  or  p. 


draft 

discount 

exchange 

freight 

guaranteed 

that  is 

merchandise 

memorandum 

Gentlemen 

take  notice 

without  discount 

number 

page 


pay't 
pd. 
per 
plcg. 
P.  0. 

payment 
paid 
by,  or  by  the 
package 
postoffice 

pr. 

pair 

pc. 
rec'd 

piece 
received 

retft 
R.  R. 

receipt 
railroad 

sliip't 
sunds. 

shipment 
sundries 

inst. 
prox. 
ult. 

present  month 
next  month 
last  month 

@ 

at 

ft 

number 

a/c 
c/o 
n/c 
o/c 

account 
care  of 
new  account 
old  account 

ACCOUNTS    AND    BILLS 


231 


419.  When  goods  are  sold  it  is  customary  for  the  creditor 
to  render  a  statement  to  the  debtor. 

On  January  2,  1900,  James  Wilson  sold  Allen  Jones  4  Ib. 
coffee  at  22^,  15  Ib.  sugar  at  6^;  Jan.  9,  2  bu.  potatoes  at  45^; 
Jan.  11,5  gal.  oil  at  80.  The  following  statement  was  made  out: 

Rochester,  N.  Y.,  Jan.  11,  1900. 


ALLEN  JONES, 


In  Account  with  JAMES  WILSON. 
(Or,  To  James  Wilson,  Dr.) 


Jan. 

2 

4  Ib.  coffee,  @  22?, 

$ 

88 

2 

15  Ib.  sugar,  @  6^, 

90 

9 

2  bu.  potatoes,  @  45^, 

90 

11 

5  gal.  oil,  @  8?, 

40 

Total, 

13 

08 

A.  S.  Ward  bought  of  H.  D.  West,  Geneva,  N.  Y.,  May  7, 
1900,  18  yd.  calico  at  9^,  20  yd.  flannel  at  60^;  May  8,  12  yd. 
gingham  at  10^;  May  14,  15  yd.  factory  at  7^,  10  yd.  cambric  at 
6^.  May  16  Ward  paid  $10.  The  following  bill  was  rendered : 

Geneva,  N.  Y.,  May  16,  1900. 


A.  S.  WARD, 


To  H.  D.  WEST,  Dr. 


May 
May 

7 
7 
8 
14 
14 

16 

18  yd.  calico,  @  9^, 
20  yd.  flannel,  @  600, 
12  yd.  gingham,  @  100, 
15  yd.  factory,  @  70, 
10  yd.  cambric,  @  60, 

Total, 
Cr. 

By  Cash, 
Balance  due, 

1  -1 
12 

1 

62 

00 

05 
60 

$13 
1 

1 

62 
20 

65 

$16 
10 

47 

00 

74 

$  6 

Receipting  Bills 

4 2O.  When  a  bill  is  paid  it  is  receipted  by  the  creditor  or 
his  agent.  When  paid  in  cash,  the  following  may  be  written 
at  the  end  of  the  bill : 

Received  payment  [or,  Paid], 

JOHN  DOE. 
Or,  Received  payment, 

JOHN  DOE, 

Per  James  Fox.  [Fox  is  agent]. 


232  MODERN    COMMERCIAL   ARITHMETIC 

When  paid  by  a  note  the  receipt  may  be : 

Received  payment  [or,  Paid]  by  note  due  Sept.  2, 
JOHN  DOE, 

Per  James  Fox. 

When  a  bill  is  not  paid,  after  "Total,"  "Balance,"  or  "Bal- 
ance due,"  the  words  "Please  remit,"  or  "Kec'd  payment," 
without  the  signature,  may  be  written. 


PROBLEMS 

Eender  and  receipt  bills  for  the  following  transactions : 

1.  R.  B.  Hillman  bought  of  Young  &  Taylor,  July  5,  1900, 
14  Ib.  steak  at  120, 18  Ib.  lard  at  100,  6  Ib.  pork  sausage  at  110; 
July  7,  20  Ib.  roast  at  130,  15  Ib.  tallow  at  70;   July  9,  4  Ib. 
steak  at  12^0,  12  Ib.  pork  chops  at  120.     July  8,  Hillman  sold 
Young  &  Taylor  a  pig  for  $4.50,  and  paid  the  balance  due 
July  10. 

2.  Stevens  &  Bacon,  Cleveland,  Ohio,  sold  R.  S.  Wall,  Aug. 
7,  1900,  4  ranges  at  $65,  5  wood  stoves  at  $18;  Aug.  10,  7  plows 
at  $6.80,  12  shovels  at  900;  Aug.  13,  6  forks  at  400.     Aug.  15, 
Wall  paid  the  bill  by  a  note  due  Dec.  8,  1900. 

8.  A.  B.  Clark,  agent  for  the  Building  Company,  Detroit, 
Mich.,  sold  Charles  Hawes,  Sept.  3,  1900,  25600  ft.  pine  floor- 
ing at  $22.50  per  M,  16700  ft.  hemlock  roofing  at  $14  per  M; 
Sept.  8,  6900  ft.  oak  joists  at  $24.75  per  M,  2150  lath  at  400 
per  C.  Sept.  6,  Hawes  sold  the  Building  Company  8500  ft. 
pine  logs  at  $9  per  M,  and  1600  ft.  hemlock  logs  at  $8  per  M, 
and  paid  the  balance  due  Sept.  12. 

4.  On  August  27,  1902,  L.  Mitchell  &  Co.,  Chicago,  sold 
to  F.  E.  Baker,  St.  Louis,  Mo.,  terms  cash,  the  follow- 
ing items:  1640  ft.  A  flooring  @  $24  per  M,  920  ft.  C  flooring 
@  $18  per  M.  2467  ft.  fencing  @  $16  per  M,  5428  ft.  scantling 
@  $13  per  M,  1432  ft.  timber  @  $9.37£  per  M,  and  860  ft. 
timber  @  $8.62£  per  M. 


ACCOUNTS   AND   BILLS 


233 


BILLS— TEADE  DISCOUNT 

New  York,  Sept.  3,  1900. 
MANNING  &  JONES,  Albany,  N.  Y., 

Bought  of  NEW  YORK  SUPPLY  COMPANY, 
Terms:  30  days;  10%  for  cash. 


Sept. 

1 
1 

200  yd.  Brussels  carpet,  @  $2.40, 
80  yd.  wool  cloth,  @  90^,  > 

$480 

72 

00 
00 

$552 

00 

3 

160  yd.  velvet  carpet,  @  $3, 

480 

00 

Less  25%, 

120 

00 

$360 

00 

Less  20%, 

72 

00 

288 

00 

Total, 

$840 

^0 

Rec'd  paym't  Oct.  1,  1900, 

NEW  YORK  SUPPLY  COMPANY. 

EXPLANATION.— The  full  cost  of  each  item  is  given.  Then  the  dis- 
count is  taken  out,  and  the  net  cost  written  in  the  proper  column.  By 
the  "Terms"  a  credit  of  30  da.  is  given.  If  the  bill  is  paid  at  date  of 
last  item  a  discount  of  10%  is  allowed.  The  bill  was  paid  and  receipted 
Oct.  1.  If  it  had  not  been  paid  by  Oct.  3  (30  da.  after  date),  it  would 
have  drawn  interest  from  that  date. 


PROBLEMS 

Render    the    following   bills   properly  discounted   and   re- 
ceipted : 

1.  H.  A.  Wood  bought  of  Sawyer  &  Jones,  Oct.  8,  1900,  on 
account  30  da. :    24  tables  at  $12.50,  less  25%   and  15%;    16 
lounges  at  $7.60,  less  30%  and  10% ;   and  12  chairs  at  $2.50, 
less  20%  and  12£%.     The  bill  was  paid  when  due. 

2.  H.  C.  Kimball  sold  to  Booth  &  Jessop,  for  cash,  Oct.  9, 
1900:    12  pianos  at  $275,  less  33£% ;    15  organs,  at  $110,  less 
25%  ;  25  violins  at  $8.50,  less  20%. 

3.  C.  D.  Beam  sold  Austin  Neff,  Oct.  11,  1900,  on  3  mo. 
credit:    200  bu.  barley  at  52^;    180  bu.  wheat  at  74^;  520  bu. 
corn  at  45^;    260  bu.  oats  at  40^.     A  trade  discount  of  20% 
was  allowed.     Neff  paid  the  bill  Nov.   11,  and  received  the 
proper  time  discount,  money  being  worth  6%. 


234  MODERN    COMMERCIAL    ARITHMETIC 

4.  C.   S.  Fanchild  bought  of  Wheeler  &  Wilson,  Buffalo, 
N.  Y.,  July  2,  1902,  2  doz.  tables  at  $2.60  each,  on  2  mo. ;  20 
sewing  machines  at  $18,  12^%  off;  4  doz.  chairs  at  750  apiece, 
on  30  da.;    8  desks  at  $45,  20%   and  12|%   off;    6  stands,  at 
$28,  15%   off.     Find  the  amount  due  Aug.   1,  1902,  money 
being  worth  6  % . 

5.  A.   C.   Taylor,    Eochester,    N.    Y.,    sold   to    Wright  & 
Young,  July  1,  1902:    12400  ft.  pine  at  $24  per  M;   4650  ft. 
chestnut  at  $45  per  M;    5900  ft.  oak  at  $38  per  M.     On  July 
15,  1902,  24300  ft.  oak  at  $35  per  M;  36500  lath  at  900  per  C; 
12420  ft.   hemlock  at  $16  per  M.      A  credit  of  30  da.   was 
allowed  and  the  bill  was  paid  Sept.  1,  1902,  interest  at  6%. 

6.  Eender  the  bill  and  find  the  amount  due  August  21, 
1902,  interest  and  discount  at  6%:    Geo.  C.  Thirp,  Chicago, 
HI.,  sold  to  W.  A.  Parsons,  May  1,  1902,  6  pc.  cotton,  60,  65, 
70,  58,  45,  75  yd.,  at  110;    8  pc.  gingham,  52,  60,  46/64,  68, 
42,  70,  55  yd.,  at   120;  June  10,   1902,  4  pc.  shirting,  40,  46, 
52,  58  yd.,  at  90;  July  23,   1902,  4  pc.  sateen,  51,  60,  73,  58 
yd.,  at  70.     A  credit  of  2  mo.  was  allowed  on  each  item. 

7.  Wetmore  &  Wales,  Cleveland,  Ohio,  sold  to  J.  C.  John- 
son, on  2  mo.  time,  10%  off  for  cash,  May  3,  1902,  15  diction- 
aries at  $5.40,  less  12|%  ;  25  atlases,  at  $4.50,  less  10%  ;  4  doz. 
geographies  at  800,  less  15%;    5  doz.  arithmetics  at  500,  less 
16f  %.     Make  out  the  bill  for  cash  payment. 

8.  The  St.   Louis,  Mo.,  Lumber  Co.   sold  M.   T.   Evans, 
April  2,  1902,  14650  ft.  pine  at  $26  per  M,  3860  ft.  clapboards 
at  $25  per  M;    May  7,  1902,  960  posts  at  $8  per  C,  11900  ft. 
flooring  at  $32  per  M,  7250  shingles  at  $3.20  per  M.     A  credit 
of   1  mo.   was  allowed,   and    discounts  of    10%    and    12|-%. 
Make  out  the  bill  for  payment  Sept.  1,  1902. 

9.  The  Metallic  Tubing  Co.,  New  York  City,  sold  1ST.  M. 
Butler,  April  18,  1902,  28  ft.  |--in.  copper  tubing  at  $1.20,  less 
15%  ;    120  ft.  1-in.  copper  tubing,  at  $1.60,  less  16f  %  ;    80  ft. 
l|-in.  steel  tubing,  at  600,  less  15%.     A  credit  of  two  months 
was  allowed.     Make  out  the  bill  for  settlement  Sept.  1,  1902, 
interest  at  6  % . 

10.  Werner  &  Jones,  Detroit,  Mich.,  sold  H.  A.  Greenwood, 


ACCOUNTS   AND    BILLS  235 

May  1,  1902,  148  yd.  silk  at  $1.30,  less  16f  % ;  45  yd.  lace  at 
800,  less  20%  ;  100  yd.  cashmere  at  250,  less  12£%  ;  320  yd. 
flannel  at  33£0,  less  20%  ;  115  yd.  lining  at  110,  less  8%  ;  200 
yd.  crash  at  60,  less  10%.  A  credit  of  30  da.  was  allowed. 
Make  out  the  bill  for  payment  Sept.  1,  1902. 

EQUATION   OF   BILLS 

421.  Debts  draw  interest  after  they  become  due. 

422.  Merchants  frequently  sell  goods  on  credit,  that  is, 
the  bill  for  payment  of  the  goods  does  not  become  due,  does  not 
draw  interest,  till  after  a  certain  period  of  time;   as,  1  mo.,  2 
mo.,  60  da.,  etc. 

423.  The  time  that  must  elapse  before  a  debt  becomes  due 
is  called  the  Term  of  Credit. 

424.  A  debt  ought  to  be  paid  when  due.     If  it  is  not  paid 
when  due,  it  should  draw  interest  from  the  time  it  is  due  till 
the  time  it  is  paid.     If  it  is  paid  before  it  is  due,  it  should  be 
discounted  for  the  time  between  the  date  of  payment  and  the 
date  when  it  becomes  due. 

425.  If  a  bill  contains  several  items  due  at  different  times, 
each  item  need  not  be  paid  as  it  falls  due,  but  the  total  of  the 
bill  may  be  paid  on  a  certain  date,  so  that  the  interest  on  the 
debts  falling  due  after  that  date  will  equal  the  discount  on 
the  debts  falling  due  before  that  date.     Payment  on  such  a 
date  would  be  just  to  both  debtor  and  creditor.     That  date  is 
called  the  due  date,  average  time,  or  equated  time. 

426.  The  Average  Time,  Equated  Time,  or  Due  Date  is 
the  date  on  which  several  debts,  or  items  of  a  bill,  may  be  can- 
celled by  one  payment. 

427.  Finding    the    equated   time   is   called   Equating  or 
Averaging  Bills. 

428.  The  process  of  finding  the  equated  or  average  time  is 
called  the  Equation,  or  Average  of  Bills. 

429.  The  time  between  the  equated  time  and  the  due  date 
of  the  earliest  payment  is  called  the  Average  Term  of  Credit. 


236 


MODERN    COMMERCIAL   ARITHMETIC 


43O.  The  time  between  the  equated  time  and  the  due  date 
of  the  latest  payment  is  called  the  Average  Term  of  Discount. 

A  owes  B  $100  to  be  paid  on  Jan.  1,  $100  to  be  paid  Jan. 
11,  and  $100  to  be  paid  Jan.  21.  When  may  he  pay  $300  and 
avoid  paying  interest?  How  does  the  interest  on  $100  from 
Jan.  1  to  Jan.  11  compare  with  the  discount  on  $100  from 
Jan.  11  to  Jan.  21? 

EXAMPLE  1. — On  Jan.  1,  1900,  N.  E.  Spenser  bought  of 
James  Hayes  mdse.  as  follows : 

Date  When  Due  Amount 

Jan.      16,  1900 $100 

Jan.      25,  1900 75 

Feb.       9,  1900 200 

March    1,  1900 150 

Total.. 


On  what  date  can  Spenser  pay  $525  and  avoid  the  payment  of 
interest? 

EXPLANATION.— If  he  pays  it  Jan.  16,  the  date  when  the  first  item 
becomes  due,  he  should  be  allowed  a  discount  on  the  other  three  items 
for  payment  in  advance.  If  he  waits  until  March  1,  the  date  when  the 
last  item  becomes  due,  he  should  pay  interest  on  the  first  three  items. 
He  wishes  to  find  a  date,  between  Jan.  16  and  March  1,  on  which  he 
may  pay  §525,  so  that  the  discount  on  the  first  items  shall  equal  the 
interest  on  the  latter  items. 

Suppose  he  does  not  pay  until  March  1,  the  due  date  of  the  last 
item.  That  would  be  the  natural  time  of  settlement.  Then  the 
amount  he  would  owe  is  shown  as  follows  (int.  at 

OPERATION 


Due  Date 

Items 

Term  of  Interest 

Interest 

Jan.      16 
Jan.      25 
Feb.        9 
March    1 

$100 
75 
200 
150 

44  da. 
35  da. 
20  da. 
0  da. 

§.73 
.44     . 
.67 
.00 

3525 

$1.84 

$525  +  $1.84  =  §526.84,  due  March  1 

How  many  days  before  March  1  should  he  pay  the  §525,  so  that  he 
will  not  have  to  pay  any  of  the  §1.84  interest?  As  many  days  as  it 
will  take  for  the  interest  on  §525  to  amount  to  31.84.  In  how  many 


ACCOUNTS   AKD   BILLS 


237 


days  will  $525  produce  $1.84  interest,  at  6%?  $1.84  -j-  $.875  (int.  on 
$525  for  1  da.)  =  21  da.  Then,  to  avoid  paying  any  interest  he  should 
pay  $525  21  da.  before  March  1,  1900.  21  da.  before  March  1  is  Feb.  8, 
which  is  the  average  time,  or  due  date,  for  paying  the  whole  amount. 
21  da.  is  the  term  of  discount. 

PROOF. — To  prove  that  Feb.  8  is  the  equated  time,  it  is  only  neces- 
sary to  show  that  the  interest  on  the  money  due  before  that  time  is 
equal  to  the  discount  on  the  money  due  after  that  time : 


Due 

Items 

Term  of  Interest  to  Feb.  8 

Interest 

Jan.      16 
Jan.      25 

$100 

75 

23  da. 
14  da. 

$.38 
.18 

$.56 

Term  of  Discount  from  Feb.  8 

Discount 

Feb.        9 
March    1 

200 
150 

1  da. 
21  da. 

$.03 
.53 

$.56 

EXAMPLE  2. — Wood  &  Wilson  sold  goods  to  J.  E.  Almj  as 
follows  : 

Jan.    4,  1900 $225 

Jan.  22 340,  on  2  mo.  credit 

Feb.    6,          160 

Feb.  27,          180,  on  60  da.  credit 

Eind  the  average  date,  or  the  date  from  which  the  whole  sum 
due  should  draw  interest. 

OPERATION 


Due  Date 

Items 

Term  of  Interest 

Interest 

Jan.        4 
March  22 
Feb.        6 
Apiil    28 

$225 
340 
160 
180 

114  da. 
37  da. 
81  da. 
Oda. 

$25.65* 
12.58 
12.96 
000 

$905 

$51.19 

*For  convenience  find  the  interest  by  the  1000-day  method,  interest 
at  36%.  That  is,  multiply  the  dollars  by  the  days  and  point  off 
three  places. 

Interest  on  $905  for  1  da.  is  $.905. 

$51.19  -*-  $.905  =  56.5  da.,  or  57  da.,  the  term  of  discount. 

57  da.  before  April  28  is  March  2,  the  average  time. 


238  MODERN    COMMERCIAL   ARITHMETIC 

EXPLANATION. — For  convenience  arrange  the  work  in  columns  as 
above.  Add  the  proper  term  of  credit  (calendar  months  when  it  reads 
mouths,  and  the  actual  number  of  days  when  it  reads  days)  to  each 
credit  item,  and  that  will  give  the  true  due  date  of  each  item.  As  in  the 
preceding  example,  assume  that  the  account  was  settled  when  the  last 
item  became  due.  The  terms  for  which  the  various  items  would  then 
draw  interest  are  114,  37,  81,  and  0  days,  respectively.  Find  the  inter- 
est on  the  items,  .by  the  1000-day  method,  at  36% .  The  total  interest  is 
$51.19.  It  will  take  as  many  days  for  $905  to  produce  $51.19  interest 
as  the  interest  on  $905  for  1  da.  is  contained  times  in  $51.19.  The 
interest  on  $905  for  1  da.  is  found  by  pointing  off  three  places.  $  905 
is  contained  56.5  times  in  $51.19.  Therefore,  $905  will  produce  $51.19 
interest  in  56.5  da.,  or  57  da.  57  da.  is  the  average  term  of  discount, 
and  57  da.  before  April  28,  or  March  2,  is  the  average  time  of  pay- 
ment. 

Steps  in  the  Operatiom. — 1.  Find  the  due  date  of  each  item 
by  adding  the  proper  term  of  credit.  When  it  reads  days,  add 
the  number  of  days;  when  it  reads  months,  add  the  number  of 
months. 

2.  Assume  a  settlement  on  the  latest  due  date,  which  is 
called  the  Focal  Date.      Find  the  term  of  interest  for  each 
item — the  number  of  days  from  each  due  date  to  the  focal  date. 

3.  Find  the  interest  on  each  item  for  its  term  of  interest, 
and  the  interest  on  the  sum  of  the  items  for  1  da. 

4.  Divide  the  total  interest  due  on  the  items  by  the  interest 
on  the  sum  of  the  items  for  1  da. 

NOTE. — Steps  4  and  5  may  be  briefly  stated :  Multiply  each  item  by 
the  term  of  interest  in  days.  Divide  the  sum  of  these  products  by  the 
sum  of  the  items. 

5.  Find  the  average  time  by  counting  back  from  the  focal 
date  the  number  of  days  in  the  average  term  of  discount. 

NOTES.— 1.  Any  date  may  be  taken  as  a  focal  date.  Some  take  the 
earliest  due  date,  and  discount  the  items  due  in  the  future  for  pay- 
ment in  advance.  But  it  is  more  in  line  with  business  practice  to  take 
the  latest  due  date  and  add  interest  to  the  items  not  paid  when  due. 
An  account  ought  to  be  settled  after  it  is  made.  It  cannot  be  settled 
before  it  is  made.  Therefore  it  is  better  to  take  the  latest  instead  of 
the  earliest  due  date  as  a  focal  date. 

2.  In  finding  the  average  term  of  credit,  a  fraction  of  a  day  of 
one-half  or  more  is  counted  as  a  full  day. 


ACCOUNTS   AND    BILLS 


-239 


PROOF 


Due 

Items 

Term  of  Interest 

Interest 

Jan.        4 
Feb.        6 

$225 
160 

57  da. 
24  da. 

$12.83 
3.84         $16.67 

Term  of  Discount 

Discount 

March  22 
April    28 

340 
180 

20  da. 
57  da. 

$  6.80 
10.26          $17.06 

The  difference  between  the  interest  and  discount  is  $.39.  The 
interest  or  discount  on  the  sum  due,  for  1  da.,  is  $.905,  therefore  the 
operation  is  correct.  It  should  be  remembered  that  the  division  in 
the  operation  of  finding  the  equated  time  in  the  example  was  not 
exact,  and  that  a  fraction  of  a  day  was  called  a  whole  day.  That  frac- 
tion of  a  day  in  the  average  term  makes  the  difference  between  the 
interest  and  the  discount  in  the  proof.  The  difference  between  the 
interest  and  the  discount  in  the  proof  should  always  be  less  than 
the  interest  on  the  debt  for  one-half  of  a  day. 

The  Product  Method 

431.  The  interest  on  the  items  for  the  terms  of  credit  by 
the  1000-day  36%  method  is  found  by  taking  the  products  of 
the  number  of  dollars  by  the  number  of  days  in  the  terms  of 
credit  and  pointing  off  3  places.  The  product  method  is  similar 
to  this  interest  method. 

EXAMPLE. — When  is  the  following  statement  due  by  equation? 

W.  A.  MILLARD, 

To  C.  E.  BIGELOW,  Dr. 


June 

2 

To  Mdse.  , 

on  30  da., 

$150 

June 

19 

ToMdse., 

220 

July 

3 

To  Mdse., 

1  mo., 

180 

July 

22 

ToMdse., 

140 

OPERATION 


Due  Date 

Items 

Term  of  Interest 

Products 

July  2 
July  19 
July  22 
Aug.  3 

$150   X 
220   X 
140   X 
180   X 

32  da.    = 
15  da.    = 
12  da.    = 
Oda.    = 

$4800 
3300 
1680 
0 

$690 

$9780 

$9780  - 
due  date. 


=  14+.      14  da.  before  Aug.  3   is  July  20,   average 


240 


MODERN   COMMERCIAL   ARITHMETIC 


EXPLANATION. — The  arrangement  of  the  work  is  similar  to  that  in 
the  interest  method.  The  latest  due  date  is  Aug.  3.  If  the  first  item 
is  not  paid  till  Aug.  3,  the  debtor  will  have  the  use  of  §150  for  32  da., 
which  is  equivalent  to  the  use  of  §150  X  32  da.,  or  §4800  for  1  da.  If 
the  items  are  not  paid  till  Aug.  3,  the  debtor  has  had  the  equivalent  of 
the  use  of  §9780  for  1  da.  He  should  pay  the  §690  long  enough  before 
Aug.  3  that  the  creditor  will  have  the  equivalent  of  the  use  of  §9780 
for  1  da.  §9780  -r-  §690  =  14+. 

If  the  debtor  pays  §690  14  da.  before  Aug.  3,  or  on  July  20th,  no 
interest  will  be  due  either  party. 

*  PROBLEMS 

When  are  the  following  bills  due  by  equation?  Prove  each 
operation : 

1.     E.  N.  BAKER, 

To  WM.  GRAY,  Dr. 


1900 

Jan. 

2 

ToMdse., 

$140 

16 

To  Mdse., 

1  mo. 

credit, 

125 

Feb. 

7 

ToMdse., 

30  da. 

credit, 

160 

26 

To  Mdse., 

60  da. 

credit, 

115 

THOMAS  GOODE, 

To  STEVENS  &  BACON,  Dr. 


1900 

Jan. 

4 

ToMdse., 

2  mo., 

$85 

29 

To  Mdse., 

145 

March 

5 

ToMdse., 

1  mo., 

175 

26 

To  Mdse., 

130 

3.     J.  H.  ROWE, 


To  JAMES  MURDOCK,  Dr. 


1900 

April 

2 

ToMdse., 

30  da., 

$120 

16 

ToMdse., 

2  mo., 

240 

May 

1 

To  Mdse., 

30  da., 

90 

24 

To  Mdse., 

118 

30 

To  Mdse., 

70 

4-     C.  A.  WOOD, 

To  POTTER  &  BOWEN,  Dr. 


1900 

May 

3 

ToMdse., 

§  70 

15 

ToMdse., 

1  mo., 

110 

June 

1 

To  Mdse., 

60  da., 

265 

11 

ToMdse., 

30  da., 

210 

30 

ToMdse., 

180 

ACCOUNTS   AND    BILLS 

5.     GEO.  CLARK, 

To  SAMUEL  TAYLOR,  Dr. 


241 


1900 

June 

3 

To  Mdse. 

3  mo., 

8275 

19 

To  Mdse. 

30  da. 

120 

28 

To  Mdse. 

60  da., 

90 

July 

5 

To  Mdse. 

310 

20 

To  Mdse. 

1  mo., 

400 

6.     J.  O.  MORGAN 

» 

To  0,  D.  WRIGHT,  Dr. 

1900 

July 

3 

To  Mdse. 

30  da., 

$230 

9 

To  Mdse. 

2  mo. 

170 

Aug. 

1 

To  Mdse. 

30  da., 

260 

17 

To  Mdse. 

30  da., 

220 

Sept. 

1 

To  Mdse. 

1  mo., 

180 

7.     H.  H.  SHORT, 

To  R.  P.  REED,  Dr. 

1900 

Sept. 

3 

To  Mdse. 

$300 

10 

To  Mdse. 

1  mo., 

150 

26 

To  Mdse. 

2  mo., 

140 

Oct. 

1 

To  Mdse. 

1  mo., 

190 

18 

To  Mdse. 

30  da., 

250 

8.     BENTON  COY, 

To 

RAYMOND  HOWE,  Dr. 

1900 

Sept. 

1 

To  Mdse. 

$430 

13 

To  Mdse. 

30  da., 

160 

29 

To  Mdse. 

1  mo., 

90 

Oct. 

22 

To  Mdse. 

130 

Nov. 

2 

To  Mdse. 

220 

EOTATION   OF   ACCOUNTS 

432.  Accounts  are  equated  in  the  same  manner  as  are 
bills,  but  in  accounts  there  is  usually  a  debit  and  a  credit  side. 

Instead  of  finding  the  amount  of  the  debit  side  as  in  a  bill, 
we  find  the  balance  of  the  two  sides.  The  equated  time  of  an 
account  is  the  time  on  which  the  balance  of  the  account  is 
due,  or  the  time  from  which  the  balance  should  draw  interest. 

The  focal  date  should  be  the  latest  due  date  in  the  account. 


242 


MODERN    COMMERCIAL   ARITHMETIC 


EXAMPLE. — What  should  be  the  face  and  the  date  of  a  note 
given  to  settle  the  following  account? 
DR.  J.  C.  BARR.  CR. 


1900 

1900 

May 

1 

To  Mdse., 

$100 

May 

14 

By  Cash, 

$  90 

May 

16 

To  Mdse., 

120 

May 

21 

By  Note, 

100 

June 

1 

To  Mdse. 

300 

June 

8 

By  Cash, 

200 

OPERATION 


Due 

Items 

Term 

Int. 

Paid 

Items 

Term 

Int. 

May    1 
May  16 
June  1 

$100 
120 
300 

38  da. 
23  da. 
7  da. 

$3.80 
2.76 
2.10 

May  14 
May  21 
June  8 

$  90 
100 
200 

25  da. 
18  da. 
0  da. 

$2.25 
1.80 
.00 

$520 
390 

$8.66 
4.05 

$390 

$4.05 

Balance, 

$130 

$4.61 

Int.  on  $130  for  1  da.  is  $.13.     $461  -5-  $.13  =  35r%,  or  35  da. 
35  da.  before  June  8  is  May  4,  the  average  date. 
The  face  of  the  note  should  be  $130,  and  the  da*te  May  4,  1900. 

PROOF 


Dr. 

Items 

Term 

Int. 

Cr. 

Items 

Term 

Int. 

May    1 
May  16 
June  1 

$100' 
120 
300 

3  da. 
12  da. 
28  da. 

$  .30  (disc.) 
1.44 
8.40 

May  14 
May  21 
June  8 

$  90 
100 
200 

10  da. 
17  da. 
35  da. 

$  .90 
1.70 
7.00 

$9.54 

$9.60 
9.54 

Balance  of  int.,     $  .06 


EXPLANATION. — Find  the  difference  between  the  discount  and  the 
interest  on  each  side,  of  the  account,  then  the  difference  of  discount  or 
interest  between  the  two  sides  should  be  less  than  one-half  of  the 
interest  or  discount  on  the  balance  of  the  account  for  one  day. 

PROBLEMS 

When  should  interest  begin  on  the  following  accounts? 
Prove  each  operation. 

1. 
DR.  ROBERT  A.  WALKER.  CR. 


1900 

1900 

Jan. 

2 

To  Mdse., 

$400 

Jan. 

4 

By  Cash, 

1300 

Jan. 

27 

To  Mdse., 

300 

Feb. 

6 

By  Cash, 

250 

ACCOUNTS   AND   BILLS 


243 


DR. 


J.  C.  MILLER. 


CR. 


1900 

1900 

May 

1 

To  Mdse., 

$200 

May 

25 

By  Note,  on  int., 

$180 

May 

12 

To  Mdse.,  30  da., 

300 

June 

12 

By  Cash, 

400 

June 

1 

To  Mdse., 

350 

July 

6 

By  Cash, 

300 

June 

18 

To  Mdse.,  2  mo., 

200 

3. 

DR.                                   A.  B.  CLAYTON.                                   CR. 

1900 

1900 

June 

4 

To  Mdse.,  30  da., 

1310 

June 

7 

By  Cash, 

$150 

June 

27 

To  Mdse.,  2  mo., 

160 

July 

3 

By  Note, 

100 

July 

6 

To  Mdse., 

150 

July 

16 

By  Cash, 

100 

Aug. 

8 

To  Mdse.  , 

240 

Aug. 

15 

By  Cash, 

120 

Aug. 

13 

To  Mdse.  , 

400 

Aug. 

20 

By  Cash, 

375 

4. 

DR.                                  L.  C.  BRADLEY.                                   CR. 

1900 

1900 

July 

6 

To  Mdse.  , 

$250 

July 

23 

By  Cash, 

$400 

July 

17 

To  Mdse.  ,  1  mo.  , 

260 

Aug. 

17 

By  Cash, 

100 

Aug. 

4 

To  Mdse.,  2  mo., 

300 

Aug. 

24 

By  Cash, 

230 

Aug. 

28 

To  Mdse., 

400 

Sept. 

4 

By  Cash, 

300 

OPERATION 


Due 

Items 

Term 

Interest 

Paid 

Items 

Term 

Interest 

July     6 
Aug.  17 
Aug.  28 
Oct.      4 

$  250 
260 
400 
300 

90  da. 
48  da. 
37  da. 
Oda. 

$22.50 
12.48 
14.80 
.00 

July    23 
Aug.   17 
Aug.   24 
Sept.     4 

$  400 
100 
230 
300 

73  da. 
48  da. 
41  da. 
30  da. 

$29.20 
4.80 
9.43 
9.00 

$12iO 
1030 

$49.78 

$1030 

$52.43 
49.78 

Balance,  $  180 

Balance,      $  2.65 

Int.  on  $180  for  1  da.  is  $.18. 

$2.65  -J-  $.18  =  14£§,  or  15  da.,  the  average  term. 

15  da.  after  Oct.  4  is  Oct.  19,  the  average  due  date. 

EXPLANATION. — This  problem  differs  from  the  preceding  only  in 
that  the  balances  of  the  items  and  the  interest  are  on  opposite  sides, 
instead  of  on  the  same  side  of  the  account.  The  balance  of  the  items 
shows  that  there  is  still  due  $180.  The  balance  of  the  interest  shows 
that  $2.65  more  interest  has  been  paid  than  is  due.  Therefore,  $180 
should  not  be  paid  until  as  many  days  after  Oct.  4  as  it  will  take  $180 
to  produce  $2.65  interest,  which  is  found  to  be  15  da. 


244 


MODERN    COMMERCIAL    ARITHMETIC 


Principle. — When  the  "balance  of  the  account  and  the  bal- 
ance  of  interest  are  on  the  same  side  of  the  account,  date  back 
from  the  focal  date;  when  the  balance  of  the  account  and  the 
balance  of  interest  are  on  opposite  sides  of  the  account,  date 
forward. 


5. 

DR.                                       H.  A.  GIBBS.                                      CR. 

1900 

1900 

Oct. 

1 

ToMdse.    1  mo., 

$200 

Oct. 

o 

By  'Cash, 

$175 

Oct. 

23 

To  Mdse. 

360 

Oct. 

10    By  Mdse., 

300 

Oct. 

30 

To  Mdse.    1  mo., 

400 

Nov. 

1    By  Cash, 

400 

Nov. 

6 

To  Mdse. 

320 

Nov. 

13 

By  Cash, 

350 

Nov. 

17 

To  Mdse. 

480 

Nov. 

19 

By  Cash, 

200 

6. 

DR.                           0          O.  S.  CONNOR.                                      CR. 

1900 

1900 

Oct. 

19 

To  Cash, 

$350 

Oct. 

4 

By  Mdse.    2  mo., 

$700 

Oct. 

30 

To  Note,  on  int.  , 

460 

Oct. 

26 

By  Mdse.    1  mo., 

100 

Nov. 

9 

To  Cash, 

400 

Nov. 

5 

By  Mdse.    1  mo., 

500 

Nov. 

21 

To  Mdse., 

520 

Nov. 

24 

By  Mdse.    1  mo., 

680 

Nov. 

30 

To  Cash, 

250 

Nov. 

29 

By  Mdse. 

230 

Dec. 

18 

To  Mdse., 

420 

Dec. 

20 

By  Mdse. 

800 

7. 

DR.                                       A.  S.  WISE.                                        CR. 

1900 

1900 

Nov. 

1 

To  Mdse.,  3  mo., 

$620 

Nov. 

9 

By  Cash, 

$200 

Nov. 

13 

To  Mdse.,  1  mo., 

175 

Nov. 

23 

By  Note,  2  mo., 

550 

Dec. 

6 

To  Mdse.,  2  mo., 

340 

no  interest, 

Dec. 

10 

To  Mdse.,  1  mo., 

450 

Dec. 

27 

By  Mdse., 

975 

Dec. 

21 

To  Mdse.. 

520 

Dec. 

29 

By  Mdse., 

140 

Dec. 

31 

To  Mdse., 

380 

Dec. 

31 

By  Cash, 

250 

8. 

DR.                                     J.   A.  NEWTON.                                     CR. 

1900 

1900 

Jan. 

4 

To  Mdse. 

$310 

Jan. 

10 

By  Note,  on  int., 

$250 

Jan. 

25 

To  Mdse. 

530 

Feb. 

6 

By  Cash., 

625 

Feb. 

9 

To  Mdse. 

160 

Feb. 

13 

By  Mdse.  , 

100 

Feb. 

26 

To  Mdse. 

315 

Feb. 

28 

By  Cash, 

240 

March 

5 

To  Mdse. 

650 

March 

7 

By  Cash, 

325 

ACCOUNTS   AND    BILLS 


245 


9. 

DR.                                 WILLARD  DOWN.                                 CR. 

1900 

1900 

May 

7 

To  Mdse.,  1  mo., 

$425 

May 

10 

By  Note,  on  int.  , 

$350 

May 

26 

To  Mdse.    2  mo., 

375 

May 

29 

By  Cash, 

400 

June 

2 

To  Mdse     1  mo., 

540 

June 

12 

By  Note,  2  mo.  , 

550 

June 

21 

To  Mdse. 

250 

no  int., 

June 

30 

To  Mdse. 

190 

July 

3 

By  Cash, 

270 

July 

6 

To  Mdse. 

460 

July 

25 

By  Cash, 

500 

10. 

DR.                                     D.  M.  SUTTON.                                    CR. 

1900 

1900 

June 

2 

To  Mdse.  ,  1  mo.  , 

$160 

June 

19 

By  Mdse.,  1  mo., 

$350 

June 

12 

To  Mdse., 

325 

June 

30 

By  Cash, 

100 

July 

6 

To  Mdse., 

250 

July 

21 

By  Cash, 

475 

July 

20 

To  Mdse., 

340 

July 

28 

By  Mdse., 

120 

Aug. 

3 

To  Mdse.  , 

520 

Aug. 

8 

By  Cash, 

450 

Aug. 

25- 

To  Mdse., 

425 

Aug. 

31 

By  Cash, 

200 

11. 

DR.                                      R.  C.  PERRY.                                      CR. 

1900 

1900 

Sept. 

1 

To  Note,  on  int.  , 

$250 

Aug. 

24 

By  Mdse.   60  da. 

$275 

Sept. 

14 

To  Mdse.,  1  mo.. 

325 

Sept. 

8 

By  Mdse.    1  mo. 

380 

Oct. 

1 

To  Cash, 

240 

Sept. 

29 

By  Mdse.  30  da. 

350 

Oct. 

19 

To  Cash, 

360 

Oct. 

9 

By  Mdse.    1  mo 

220 

Oct. 

30 

To  Cash, 

150 

Oct. 

27 

By  Mdse.    1  mo. 

460 

Nov. 

20 

To  Cash, 

280 

Nov. 

13 

By  Mdse. 

150 

12.  Find  the  balance  of  the  following  account,  when  the 
balance  was  due  by  equation,  and  what  the  balance  amounted 
to  if  nob  paid  until  June  1,  1900,  money  being  worth  6%  : 
DR.  D.  A.  BROOKS.  CR. 


1900 

1900 

Jan. 

4 

To  Mdse., 

$300 

Jan. 

9 

By  Cash, 

$200 

Jan. 

18 

To  Mdse., 

160 

Jan. 

25 

By  Cash, 

240 

Feb. 

1 

To  Mdse., 

420 

Feb. 

10 

By  Cash, 

360 

Feb. 

16 

To  Mdse.  , 

350 

Feb. 

28 

By  Cash, 

210 

IS.  Find  when  the  balance  of  the  following  account  was 
due,  and  what  was  paid  to  settle  the  account    April  1,  1900, 
interest  at  6  %  : 
DR.  HAMILTON  SEAMANS.  CR. 


1900 

1900 

Feb. 

2 

To  Mdse.,  1  mo., 

$275 

Feb. 

8 

By  Mdse.,  1  rno., 

$190 

Feb. 

13 

To  Mdse.,  1  mo., 

360 

March 

1 

By  Cash, 

275 

March 

9 

To  Mdse.  , 

430 

March 

20 

By  Cash, 

260 

March 

28 

To  Mdse., 

110 

March 

30 

By  Cash, 

235 

246 


MODERN   COMMERCIAL  ARITHMETIC 


l^.  Equate  the  following  account : 
DR.  J.  P.  WORTH. 


CR. 


1900 

II       1900 

Jan. 

5 

ToMdse., 

§300 

Jan. 

9 

By  Cash, 

$260 

Jan. 

23 

To'Mdse., 

250 

Jan. 

30 

By  Cash, 

180 

Feb. 

8 

To  Mdse., 

175 

Feb. 

13 

By  Note,  1  mo., 

350 

no  int., 

Feb. 

37 

To  Mdse., 

400 

March 

8 

By  Cash, 

335 

OPERATION 


Due 

Horns 

Term 

Interest 

Paid 

Items 

Term 

Interest 

Jan.      5 
Jan.    23 
Feb.     8 
Feb.    27 

$  300 
250 
175 
400 

67  da. 
49  da. 
33  da. 
17  da. 

$20.10 
12.05 

5.78 
6.80 

Jan.        9 
Jan.      30 
March  13 
March   8 

$  260 
180 
350 
335 

63  da. 
14  da. 
Oda. 
5  da. 

$16.38 
2.52 
0.00 
1.68 

$1125 
1125 

$44.73 
20.58 

$1125 

$20.58 

$24.15 

$24.15  -j-  6  =  $4.03,  balance  due  March  13. 

EXPLANATION. — There  is  no  balance  in  this  account,  the  two  sides 
being  equal,  but  there  is  an  interest  balance  of  $24. 15  on  the  Dr.  side, 
which  shows  that  that  amount  should  be  paid  or  added  to  the  Cr. 
side.  But  the  interest  as  here  reckoned  is  at  36  %  -  Since  the  true  rate 
is  $%,  divide  $24.15  by  6,  and  the  quotient  will  show  the  interest 
balance  due  March  13,  1900. 


15.  Equate  the  following  account,  interest  at  4%  : 


DR. 


L.  M.  BEEKMAN. 


CR. 


1900 

1900 

Feb. 

3 

ToMdse., 

8250 

Feb. 

6 

By  Cash, 

$170 

Feb. 

21 

ToMdse., 

160 

Feb. 

26 

By  Cash, 

190 

March 

7 

To  Mdse., 

300 

March 

14 

By  Mdse., 

400 

March 

31 

ToMdse., 

270 

Apr. 

4 

By  Cash, 

200 

Apr. 

9 

To  Mdse., 

400 

Apr. 

25 

By  Cash, 

420 

ACCOUNTS   CURRENT 

433.  A  statement  of  a  running  account  showing  the  debits 
and  credits  and  the  cash  balance,  with  interest  or  discount  to 
date,  is  called  an  Account  Current. 


ACCOUNTS    AND    BILLS 


247 


434.  Adjusting  an  account  is  finding  the  cash  balance  due 
at  a  given  date. 

435.  Theoretically,  all  sums  due  draw  interest,  and  all 
sums  paid  before  they  are  due  are  subject  to  discount. 

Most  retail  dealers  do  not  charge  interest  on  the  items  of  a 
running  account,  but  the  balance  of  a  closed  account  draws 
interest  from  the  date  of  the  last  item. 

Custom  or  agreement  between  wholesale  dealers  determines 
whether  the  items  of  a  running  account  draw  interest.  It  is 
customary  to  charge  interest  on  such  items  after  a  certain  term 
of  credit. 

436.  Equating  an  account  is  finding  at  what  date  the  bal- 
ance is  due.     Adjusting  an  account  is  finding  the  balance  due 
at  a  given  date. 

EXAMPLE. — Find  the  balance  due  on  the  following  account 
June  1,  1900,  interest  at  6%. 


DR. 


R.  H.  KNAPP. 


CR. 


1900 

1900 

March 

6 

To  Mdse.,  1  mo., 

$350 

March 

21 

By  Cash, 

$200 

March 

29 

ToMdse.,  2  mo., 

400 

Apr. 

16 

By  Mdse.,  1  mo., 

360 

Apr. 

7 

To  Mdse., 

200 

May 

3 

By  Cash, 

270 

Apr. 

25 

ToMdse.,  2  mo.. 

250 

May 

26 

By  Mdse.  ,  1  mo.  , 

300 

OPERATION 


Due 

Items 

Term 

Int. 

Disc. 

Paid 

Items 

Term 

Int. 

Disc. 

April    6 
May    29 
April    7 
June  V25 

$  350 
400 
200 
250 

56  da 
3  da. 
55  da. 
24  da. 

$3.27 
.20 
1.83 

$1.00 

Mar.  21 
May  16 
May    3 
June  26 

$  200 
360 
270 
300 

72  da. 
16  da. 
29  da. 
25  da. 

$2.40 
.96 
1.31 

$1.25 

81200 

$5.30 

$1.00 

$1130 

$4.67 

$1.25 

$1200  +  $5.30  —  $1  =  $1204.30.     $1130  +  $4.67  —  $1.25  =  $1133.42. 

$1204.30  —  $1133.42  =  $70.88,  balance  due  June  1,  1900. 

EXPLANATION.— Find  the  interest  on  each  item  from  the  day  it  is 
due  to  the  day  of  settlement.  If  an  item  falls  due  after  the  date  of 
settlement,  it  should  be  discounted,  and  the  discount  should  be  taken 
from  the  amount  due  at  the  date  of  settlement.  The  sum  of  the  items, 
plus  the  interest,  less  the  discount,  is  the  total  amount  of  either  side 
of  the  account. 


248 


MODERN    COMMERCIAL    ARITHMETIC 


PROBLEMS 

1.  Find  the  balance  due  May  1,  1900: 
DR.  A.  L.  KINNEY. 


CR. 


1900 

1900 

Feb. 

2 

To  Mdse.,  2  mo. 

§420 

Feb. 

5 

By  Mdse.,  1  mo., 

1360 

Feb. 

21 

To  Mdse.,  1  mo. 

250 

Feb. 

24 

By  Cash, 

240 

March 

3 

To  Mdse.,  1  mo. 

160 

M  arch 

16 

By  Cash, 

150 

March 

20 

To  Mdse.,  1  mo. 

380 

March 

27 

By  Mdse.  ,  1  mo.  , 

400 

March 

24 

To  Mdse.,  1  mo. 

300 

Apr. 

17 

By  Cash, 

200 

2.  What  is  the  balance  due  June  1,  1900? 
DR.  F.  A.  SAYRE. 


CR. 


1900 

1900 

March 

6 

To  Mdse., 

§225 

March 

19 

By  Mdse.  ,  2  mo.  , 

§350 

March 

21 

To  Mdse., 

500 

Apr. 

6 

By  Cash, 

400 

Apr. 

14 

To  Mdse., 

340 

Apr. 

25 

By  Mdse.,  2  mo., 

650 

May 

5 

To  Mdse..  1  mo., 

720 

May 

11 

By  Cash, 

450 

May 

23 

To  Mdse.,  1  mo., 

400 

May 

25 

By  Cash, 

300 

3.  What  is  the  balance  due  Sept.  1,  1900? 
DR.  J.  H.  HADLEY. 


CR. 


1900 

1900 

June 

2 

To  Mdse. 

§150 

June 

7 

By  Cash, 

§100 

June 

20 

To  Mdse. 

270 

June 

29 

By  Cash, 

175 

July 

11 

To  Mdse. 

500 

July 

6 

By  Mdse.,  1  mo., 

600 

July 

23 

To  Mdse. 

120 

July 

27 

By  Cash, 

100 

Aug. 

4 

To  Mdse. 

310 

Aug. 

1 

By  Mdse., 

250 

Aug. 

22 

To  Mdse. 

230 

Aug. 

29 

By  Cash, 

200 

4.  What  is  the  balance  due  Oct.  1,  1900? 
DR.  C.  F.  CHASE. 


CR. 


1900 

1900 

July 

7 

To  Mdse., 

§350 

July 

2 

By  Mdse.,  1  mo., 

§400 

July 

28 

To  Mdse., 

540 

July 

17 

By  Mdse.,  1  mo., 

250 

Aug. 

9 

To  Mdse., 

200 

Aug. 

1 

By  Cash, 

100 

Aug. 

29 

To  Cash, 

100 

Aug. 

15 

By  Mdse.,  1  mo., 

500 

Sept. 

8 

To  Cash, 

400 

Sept. 

5 

By  Mdse.,  1  mo., 

350 

Sept. 

26 

To  Cash, 

200 

Sept. 

21 

By  Mdse.,  1  mo., 

220 

ACCOUNTS   AND   BILLS  249 

ACCOUNT    SALES 

437.  A  statement  rendered  by  an  agent,  showing  his  sales 
for  his  principal,  his  charges  against  the  principal,  the  amount 
previously  remitted  (if  any),  and  the  amount  due  at  the  equated 
date,  or  the  amount  due  at  a  given  date,  is  called  an  Account 
Sales. 

438.  The  agent's  gross  sales  constitute  the  credits  of  the 
account,  and  his  charges  constitute  the  debits. 

439.  The  agent  frequently  guarantees  the  quality  of  the 
goods  he  sells  for  his  principal,  for  which  he  is  allowed  a  com- 
pensation   called    Guaranty.     Guaranty,  like    commission,    is 
computed  at  a  certain  rate  per  cent  on  the  sales. 

440.  The  agent's  charges  include  commission,  guaranty, 
freight,  cartage,  storage,  insurance,  etc. 

441.  An  account    sales   may  be   rendered   simply  as   an 
equated  account  or  as  an  account  current.     That  is,  it  may 
show  the  balance  due  on  the  equated  date  or  on  a  given  date. 

Items  of  freight,  cartage,  storage,  and  insurance  are  ren- 
dered as  due  on  the  date  the  agent  paid  them. 

Commission  and  guaranty  are  sometimes  considered  as  due 
on  the  date  the  account  is  rendered,  sometimes  on  the  date  of 
the  last  sale,  sometimes  on  the  date  of  each  sale,  sometimes  on 
the  average  date  of  the  sales,  and  sometimes  on  the  average 
due  date  of  the  sales.  When  sales  are  made  on  credit,  the 
average  date  of  sales  is  not  the  same  as  the  average  due  date  of 
the  sales. 

An  account  sales  is  equated  or  adjusted  like  any  other 
account. 

PROBLEMS 

1.  W.  S.  Davis,  Chicago,  111.,  sold  lumber  for  Aldridge  & 
Bro.,  Milwaukee,  Wis.,  as  follows:  Jan.  3,  1900,  24000  ft. 
hemlock  at  $13  per  M;  Jan.  9,  59000  ft.  pine  at  $24  per  M; 
Jan.  26,  18500ft.  chestnut  at  $42  per  M;  Feb.  5,  27300  ft. 
oak  at  $40.50  per  M;  Feb.  13,  35700  ft.  pine  at  $23  per  M. 
The  agent  paid  for  freight,  on  Jan.  2,  $275 ;  $62  for  storage, 


250 


MODERN    COMMERCIAL   ARITHMETIC 


on  the  date  of  the  last  sale;  Jan.  29,  he  advanced  $2500.  His 
commission  was  4%,  due  on  the  average  date  of  sales.  He 
rendered  his  account  sales  Feb.  17,  1900.  Reproduce  the 
account. 

2.  Find  the  balance  of  the  following  account  sales,  and 
when  due  by  equation.  Consider  the  entire  commission  due 
on  the  date  of  the  last  sale: 

New  York  City,  Nov.  7,  1900. 
Account  Sales  of  Apples, 

For  %   of  WILSON  &  CO., 

Buffalo,  N.  Y. 
ByJ.  C.  FOWLER. 


1900 

Oct. 

5 

SALES  (CR.) 
240  bbl.  Snow,  @  $2.10,  cash, 

10 

350  bbl.  King,  @  $1.85,  1  mo., 

16 

180  bbl.  Greening,  @  $1.50,  1  mo  , 

Nov. 

7 

400  bbl.  Baldwin,  @  $1.60,  cash, 

Total,  Cr., 

Oct. 
Nov. 

1 
15 
23 
6 

7 

CHARGES  (DR.) 
Freight, 
Cartage, 
Cash  advanced, 
Storage, 
Commission  and  guaranty,  3$>, 

$525 
48 
800 
40 

00 
00 
00 
00 

Total,  Dr., 

Net  proceeds, 
Due  ,  1900. 

3.  Find  the  net  proceeds  and  when  due  of  the  following 
account  sales : 


1902 

SALES  (Cn.) 

July 

3 

25  bbl.  Pork,  @  $12.80,  30  da., 



July 

*>$ 

45  bbl  Pork   (a)  $12  60  cash 

Am? 

0 

40  bbl  Pork   @  $13  00,  20  da., 

Auer. 

17 

30  bbl.  Pork,  @  $12.85,  10  da., 

Tnfal    fV 



CHARGES  (DR.) 

July 

1 

Freight, 

$  71 

40 

July 

1 

Cash  advanced, 

250 

00 

Commission  (due  ),  4$>, 

Total,  Dr., 

Net  proceeds, 

PARTNERSHIP 

PARTITIVE  PROPORTION 

442.  Partitive  Proportion  is  the  process  of  dividing  a  num- 
ber into  parts  proportional  to  two  or  more  given  numbers. 

PROBLEMS 

1.  A  worked  3  days  and  B  4  days,  for  the  same  daily  pay. 
Altogether  they  received  $14.     What  was  the  daily  wages  of 
each? 

2.  Two  men  performed  a  piece  of  work  for  $40.     The  first 
agreed  to  take  $3  for  every  $5  received  by  the  second.     How 
much  did  each  receive? 

3.  Divide  $60  into  parts  proportional  to  2,  4,  and  6. 

4.  Divide  $216  into  parts  which  shall  be  to  one  another  as 
5,  6,  and  7. 

5.  Divide  750  into  parts  proportional  "to  10,  15,  and  25. 

6.  A,  B,  and  C  put  their  sheep  into  one  flock  and  agreed  to 
sell  them  at  a  common  price.     A  put  in  40  sheep,  B  put  in  70 
sheep,  and  C  put  in  85  sheep.     They  sold  the  flock  for  $1170. 
What  did  each  man  receive? 

7.  A  has  $500,  B  $600,  and  C  $400  invested  in  a  business. 
What  fractional  part  of  the  gain  ought  each  to  receive?     If  the 
whole  gain  is  $150,  what  will  be  A's  share? 

8.  Two  men  engage  in  business.     A  puts  in  $150,  and  B 
puts   in  $270.      If   they  gain   $210,  how  much   should   each 
receive? 

9.  Three  men  invest  the  following  sums  in  a  store:  $1200, 
$1400,  $1800.    If  they  gain  $550,  what  sum  should  each  receive? 

10.  Divide  75  into  parts  proportional  to  %  and  £. 

NOTE — Fractions  to  be  compared  must  have  a  common  denom- 
inator. Then  they  are  to  each  other  as  their  numerators.  £  and  J  are 
equivalent  to  f  and  |,  and  are  to  each  other  as  3  and  2.  Therefore, 
divide  75  into  parts  proportional  to  3  and  2. 

251 


252  MODERN    COMMERCIAL   ARITHMETIC 

11.  Divide  72  into  parts  proportional  to  £  and  \. 

12.  Divide  470  into  parts  proportional  to  3£  and  4£. 

13.  Divide  $1105  into  parts  proportional  to  f ,  f ,  and  £. 

14.  Divide  $373.10  into  parts  proportional  to  1475,  1325, 
and  2530. 

15.  Divide  $405  into  parts  proportional  to  f ,  f ,  and  f . 

PARTNERSHIP 

443.  An  association  formed  by  two  or  more  persons  invest- 
ing capital  in  a  business  and  agreeing  to  share  the  gains  and 
losses  of  the  business  is  called  a  Partnership. 

444.  The  persons  that  form   the   association   are   called 
Partners.     Collectively,  they  are  called  a  Company,  Firm,  or 
House. 

445.  The  capital  invested  may  be  money,  other  property, 
or  labor. 

440.  The  gains  and  losses  of  a  partnership  are  shared  in 
proportion  to  the  value  of  the  capital  invested  and  the  time 
the  capital  is  employed. 

447.  Eesources,  or  Assets,  consist  of  the  property  of  the 
firm  and  the  debts  due  the  firm. 

448.  Liabilities  are  the  debts  of  a  firm. 

449.  The  Net  Capital  is  the  excess  of  the  assets  over  the 
liabilities. 

450.  The  Net  Insolvency  is  the  excess  of  the  liabilities  over 
the  assets. 

451.  With  respect  to  their  manner  of  connection  with  a 
firm,  there  may  be  four  kinds  of    partners:    real,   dormant, 
nominal,  limited. 

452.  A  Real,  or  Ostensible  Partner,  is  one  who  has  cap- 
ital invested,  and  is  simply  a  partner  without  restrictions  or 
conditions. 

453.  A  Dormant,  or  Silent  Partner,  is  one  who  has  capital 
invested,  but  who  tries  to  conceal  the  fact  and  does  not  appear 
to  the  public  as  a  partner. 


PARTNERSHIP  253 

454.  A  Limited  Partner  is  one  who  gives  legal  notice,  by 
publication,  of  the  limit  of  his  responsibility  for  the  debts  of 
the  firm. 

455.  A  Nominal  Partner  is  a  partner  in  name  only.     He 
has  no  capital  invested,  and  allows  the  use  of  his  name  as  a 
partner  simply  to  give  prestige  to  the  firm. 

456.  A  real  partner  is  liable  for  all  the  debts  of  the  firm. 
A  silent  partner  is  also  liable  for  the  debts  of  the  firm,  but  he 
cannot  be  held  responsible  unless  his  connection  with  the  firm 
is  known.     A  limited  partner  is  liable  to  a  limited  extent.     A 
nominal  partner  is  liable  for  the  debts  of  the  firm  to  all  persons 
who  have  trusted  the  firm  because  such  partner  was  a  member 
of  the  firm.     If  persons  are  deceived  by  a  nominal  partner,  the 
partner  should  pay  for  the  deception. 

EXAMPLE. — A,  B,  and  C  formed  a  partnership.  A  fur- 
nished $4000  of  the  capital,  B  $6000,  and  0  $8000.  If  they 
gained  $1440,  what  was  each  partner's  share  of  the  gain? 

OPERATION 
$4000  +  $6000  +  $8000  =  $18000,  total  capital 

yVoVo  or  I  =  A's  share  of  the  capital 
TYoVV  or  |  =  B's  share  of  the  capital 
T\V<ro  or  f  =  C's  share  of  the  capital 
f  of  $1440  =  1320,  A's  share  of  the  gain 
4  of  $1440  =  $480,  B's  share  of  the  gain 
•f  of  $1440  =  $640,  C's  share  of  the  gain 

Or,     $4000  +  $6000  4-  $8000  =  $18000,  total  capital 

$1440  =  net  gain 

$1440  -  $18000  =  .08,  or  8  per  cent  gain 
8%  of  $4000  =  $320,  A's  gain 
8%  of  $6000  =  $480,  B's  gain 
8%  of  $8000  =  $640,  C's  gain 

PROBLEMS 

1.  Jones,  Smith,  and  Brown  formed  a  partnership,  Jones 
putting  in  $7000  of  the  capital,  Smith  $5000,  and  Brown  $9000. 
If  they  gained  $2940,  what  was  each  one's  profit? 


254  MODERN   COMMERCIAL   ARITHMETIC 

2.  Beekman,   Hadley,   and   Perry  entered    a   partnership, 
Beekman  furnishing  $12000  capital,  Hadley  $8000,  and  Perry 
$11000.     If  they  lost  $1240,  what  was  each  partner's  loss? 

3.  Two  men  bought  a  farm  for  $15000,  one  paying  $9000 
and  the  other  $6000.     If  they  sold  the  farm  for  $17500,  what 
was  the  gain  of  each? 

4.  The  total  assets  of  the  firm  of  Watson  &  Barnes  are 
$18700,  and  the  liabilities  are  $4200.     Watson  invested  $5400, 
and  Barnes  invested  $6300.     Find  the  net  gain  and  the  present 
worth  of  each  partner. 

5.  Pour  partners  invested  as  follows:    A  $4800,  B  $7200, 
C  $6000,  D  $8400.     After  one  year  their  resources  are  $32270, 
and  their  liabilities  are  $2570.      Pind  the  present  worth  of 
each  partner. 

6.  Gooding  and  Spenser  formed  a    partnership,   Gooding 
investing  $21000  and  Spenser  $17000.     After  two  years  they 
dissolved  partnership  with  the  following  resources  and  liabilities : 

Resources  Liabilities 

Mdse.,  per  inventory .  $  9600  Mortgage $2000 

Cash 6260           Accounts  payable  . . .     1500 

Accounts  receivable  .  12300 

Real  estate 15500 

Find  the  present  worth  of  each  partner 

7.  Hawes  &  Cross  bought  a  mill  for  $60000,  Hawes  paying 
$35000  and  Cross  $25000.     Newcomb  paid  them  $40000  for  a 
one-third  interest  in  the  mill.      What  part  of  the  mill  did 
Hawes  and  Cross  each  own?    What  part  of  the  $40000  did  each 
receive?     If,  after  the  sale,  each  had  been  credited  with  a  one- 
third  interest  in  the  mill,  what  part  of  the  $40000  ought  Hawes 
to  have  received? 

8.  A  began  business  with  a  capital  of  $15000.     After  3  mo. 
he  took  in  B  as  a  partner  with  $12000,  and  3  mo.  later  they 
took  in  C  with  $16000.     If  the  total  gain  for  the  year  was 
$2592,  what  was  each  partner's  share? 


PARTNERSHIP  255 

OPERATION 

A's  capital  =  $15000  employed  for  12  mo.  =  $180000  for  1  mo. 

B's  capital  =    12000  employed  for    9  mo.  =    108000  for  1  mo. 

C's  capital  =    16000  employed  for    6  mo.  =      96000  for  1  mo.  * 

Total  capital  employed  for    1  mo.  =    384000 

A's  share  of  capital  =  HH##»  or  H 

B's  share  of  capital  =  HfJHHK  or  A 

C's  share  of  capital  =  ^W&,  or  J 

A's  share  of  gain      =  ££  of  $2592,  or  $1215 

B's  share  of  gain      =  &  of    2592,  or      729 

C's  share  of  gain      =  £  of    2592,  or      648 

9.  Martin,  Gould,  and  Towne  formed  a  partnership.     Mar- 
tin invested  $12000  for  15  mo.     He  also  worked  9  mo.,  and  his 
labor  was  counted  equivalent  to  the  use  of  $10000.     Gould 
invested  $21000  for  10  mo.,  and  Towne  put  in  $18000  for  8 
mo.,  and  $12000  more  for  9  mo.     The  total  gain  was  $5160. 
Find  each  partner's  share. 

10.  Howe,  Benton,  and  Ward  formed  a  partnership  Jan.  1, 
each   investing  property  valued  at  $5000.      March  1?  Howe 
added  $1500,  and  June  1  he  added  $800.     April  1,   Benton 
added  $1200,  and  Oct.  1  he  added  $900.     July  1,  Ward  drew 
out  $500,  and  Sept.  1  he  added  $800.     If  the  gain  for  the  year 
was  $1250,  what  was  each  partner's  share? 

11.  Bush,   Austin,   and  Fox  rented    a  pasture  for   $400. 
Bush  pastured  200  sheep  for  3  mo.,  Austin  300  sheep  for  4 
mo.,  and  Fox  250  sheep  for  2  mo.     What  rent  should  each 
man  pay? 

12.  Johnson  and  Chapin  bought  3  houses  of  equal  value  for 
12000,  Johnson  paying  $1200,  and  Chapin  $800.     Wilson  paid 
them  $1500  for  one  of  the  houses.     If  Johnson  and  Chapin 
each  took  one  of  the  other  two  houses,  what  part  of  the  $1500 
ought  each  to  receive? 

18.  Wright,  Greene,  and  Bates  formed  a  partnership  to 
continue  three  years,  each  investing  $10000.  After  8  mo., 
Wright  invested  $1200  more,  and  Greene  drew  out  $900;  4  mo. 
later  Bates  invested  $1500,  and  Wright  withdrew  $500;  18  mo. 
before  dissolution  Thompson  was  admitted  to  the  firm  with  a 


256  MODERN"   COMMERCIAL   ARITHMETIC 

capital  of  $6000,  and  1  yr.  before  dissolution  each  partner 
withdrew  $800.  At  the  time  of  dissolution  the  resources  and 
liabilities  of  the  firm  were  as  follows : 

Resources  Liabilities 

Mdse. $12400           Notes $1750 

Cash 8000            Mortgage 2000 

Bills  receivable 21500            Rent  due 500 

Real  estate 12000            Bills  payable 3650 

What  was  the  present  worth  of  each  partner  at  the  close  of  the 
partnership? 

14.  Eandall  and  Chapman  formed  a  partnership  Jan.  1, 
1898,  each  investing  $7000.  April  1,  1898,  Randall  drew  out 
$500,  and  Chapman  added  $1200.  Sept.  1,  1898,  they  took  in 
Holt  with  a  capital  of  $6000.  Jan.  1,  1899,  Chapman  invested 
$1000  more,  and  Randall  drew  out  $800.  April  1,  1899,  Holt 
added  $1500  and  Randall  $1200.  Oct.  1,  1899,  each  partner 
withdrew  $900.  At  time  of  settlement  $2000  was  allowed  Eandall 
for  salary.  On  January  1,  1900,  the  firm  sold  out  for  $22500.  If 
no  salary  had  been  paid  Randall,  how  should  the  money  be 
divided? 


STOCKS  AND  BONDS 

457.  A  company  that  has  a  charter  that  defines  the  legal 
powers  of  the  company  is  called  a  Corporation. 

When  a  large  sum  of  money  is  necessary  to  carry  on  a  busi- 
ness, usually  a  number  of  persons  contribute  money  and  form  a 
corporation. 

458.  The  total  sum  contributed  (in  money  or  in  property) 
is  called  the  Capital  Stock  of  the  corporation. 

459.  The  capital  stock  is  divided  into  equal  parts  called 
Shares.     The  par  value  of  a  share  is  usually  $100. 

460.  Each   contributor  receives  a  Stock   Certificate.      It 
states  the  number  of  shares  of  stock  which  he  owns  and  the  par 
value  of  a  share. 

461.  The  value  of  jt  share  of  stock  stated  in  the  certificate 


i^fche  Par  Value  of  the  stock. 

,462.  If  the  business  of  a  corporation  proves  profitable,  at 
thd^end  of  a  year,  six  ninths,  or  some  other  stated  period  of 
tim\$,  the  corporation  divides  the  net  gain  among  the  stock- 
holders in  proportion  to  the  number  of  shares  which  they  hold. 
This  sum  divided  is  called  the  Dividend  of  the  corporation. 
The  part  received  by  each,  stockholder  is  his  dividend.  A  cor- 
poration may  pay  annual,  semi-annual,  or  quarterly  dividends. 

When  a  dividend  is  declared  by  a  corporation,  it  is  stated  as 
a  per  cent  of  the  capital  stock.  Thus,  if  a  corporation  with  a 
capital  stock  of  $1000000  has  $100000  gain  to  divide  among  its 
stockholders,  it  declares  a  dividend  of  10%. 

463.  If  the  business  proves  unprofitable  for  any  period  for 
which  a  dividend  is  usually  declared,  the  corporation  taxes,  or 
assesses,  each  stockholder  for  his  share  of  the  net  loss.  The 
sum  a  stockholder  must  pay  to  meet  the  losses  of  the  corpora- 
tion is  an  assessment.  Thus,  a  corporation  may  declare  an 
assessment  of  5%. 

257 


258  MODERN    COMMERCIAL   ARITHMETIC 

464.  The  annual  rate  of  interest  on  money  loaned  is  usually 
from  4%  to  6%.     If  a  corporation  pays  an  annual  dividend  of 
10%,  people  who  have  money  to  loan  or  invest  will  want  to  buy 
shares  of  stock  of  that  company,   because   they  would   then 
receive  a  higher  rate  of  income  on  their  money.    In  such  a  case, 
the  stockholders  will  be  able  to  sell  their  shares  for  more  than 
$100  (or  the  par  value).     Thus,  a  share  of  stock  whose  par 
value  is  $100  may  be  sold  for  $120. 

465.  When  stock  sells  for  more  than  its  par  value,  it  is 
said  to  be  Above  Par,  or  At  a  Premium. 

If,  however,  a  corporation  declares  an  assessment  or  a  very 
low  dividend,  the  stockholders  may  desire  to  sell  their  shares  of 
stock  and  invest  the  proceeds  in  a  more  profitable  business. 
Thus,  a  share  of  stock  whose  par  value  is  $100  may  be  sold 
for  $95. 

466.  When  stock  sells  for  less  than  its  par  value,  it  is  said 
to  be  Below  Par,  or  At  a  Discount. 

467.  In  each  large  city  there  is  a  Stock  Exchange,  which 
is  an  association  of  dealers  in  stocks  of  corporations. 

The  shares  of  stock  of  the  corporations  are  put  upon  the 
market  and  are  bought  and  sold  in  the  various  stock 
exchanges. 

468.  A  person  who  buys  or  sells  stocks  for  another  at  a 
stock  exchange  is  called  a  Stock  Broker. 

469.  The  value  of  a  share  of  stock  as  determined  by  the 
price  for  which  it  will  sell  in  the  market  is  called  its  Market 
Value. 

470.  A    corporation    may  issue    common   and  preferred 
stock. 

471.  Preferred  Stock  is  that  which  draws  certain  guaran- 
teed  dividends.       Common   Stock   draws    such   dividends    as 
remain  after  the  dividends  on  the  preferred  stock  have  been 
paid. 

Preferred  stock  is  usually  issued  to  persons  who  buy  shares 
of  stock  when  the  corporation  is  in  need  of  money. 


STOCKS    AND    BONDS  259 

PROBLEMS 
NOTE. — Unless  otherwise  mentioned,  a  share  is  $100. 

1.  If  a  corporation  declares  an  annual  dividend  of  8%,  what 
dividend  will  a  stockholder  receive  who  owns  36  shares? 

2.  A  corporation  levied  an  assessment  of  4%.     What  assess- 
ment was  paid  by  a  holder  of  115  shares  of  stock? 

8.  A  telegraph  company  declared  dividends  of  12%  on  pre- 
ferred stock  and  9%  on  common  stock.  What  dividend  was 
received  by  a  holder  of  48  shares  of  preferred  and  25  shares  of 
common  stock? 

4.  A  manufacturing  company  declared  a  dividend  of  6%  on 
preferred  stock  and  1%  on  common  stock.     Find  the  income 
from  26  shares  of  preferred  stock  and  50  shares  of  common 
stock. 

5.  A  bank  with    $2650000  capital  stock   divided  $145750 
among    its    stockholders.      What   was   the   rate   of    dividend 
declared? 

6.  A  railroad  company  lost  $35550  on  a  capital  stock  of 
$1580000.     What  rate  of  assessment  was  necessary  to  cover  the 
loss? 

7.  A  man  invested  $8500  in  stock  at  par,  and  drew  an 
annual   dividend  of  $552.50.      What  rate  of  income  did  he 
receive  on  his  investment?     If  money  is  worth  6%,  would  the 
market  value  of  his  stock  be  above  or  below  par? 

8.  What  is  the  cost  of  125  shares  of  bank  stock  at  114£, 
brokerage  -J%. 

NOTE. — The  pay  a  broker  receives  is  called  Brokerage.  A  broker 
usually  charges  I  %  of  the  par  value  of  the  stock  for  buying  or  selling 
the  same.  Brokerage  is  computed  upon  the  par  value  of  the  stock. 

9.  Find  the  cost  of  218  shares  of  Central  R.  R.  stock  at 
138^,  brokerage  -£%. 

10.  What  will  be  the  cost  of  62  shares  of  mining  stock  at  93, 
brokerage  -J-%? 

11.  I  sold  120  shares  of  Erie  R.  R.   stock  at  70,  paying 
brokerage  at  -J-%.     How  much  did  I  receive? 


260  MODERN    COMMERCIAL   ARITHMETIC 

12.  A  speculator  bought  240  shares  L.  V.  R.  R.  stock  at 
105£,  and  sold  it  at  110.     How  much  did  he  gain,  brokerage 
in  each  case  being  £%? 

13.  Find  the  cost  of  115  shares  of  stock  at  9J%  premium, 
brokerage  J%? 

14.  What  must  be  paid  for  90  shares  of  stock  at  H-2-%  pre- 
mium, brokerage  -J-%? 

15.  How  many  shares  of  stock  at  110  can  be  bought  for 
$3524,  if  £%  is  paid  for  brokerage? 

OPERATION 

1  share  costs  $110£ 
$3524  -4-  $110£  =  32  shares 


16.  How  many  shares  of  oil  stock,  at  108,  can  be  bought 
for  $6055,  brokerage  |%? 

17.  A  man  exchanged  24  shares  of  bank  stock,  at  98,  for 
railroad  stock  at  84.     How  many  shares  did  he  receive? 

18.  How  many  shares  of  stock  must  be  sold  at  97,  brokerage 
£%,  to  obtain  $4662? 

19.  I  bought  140  shares  of  stock  at  3%  premium.     At  what 
price  must  I  sell  it  to  gain  $721? 

'20.  What  annual  income  will  be  realized  from  an  invest- 
ment of  $3610  in  6%  preferred  stock,  bought  at  95? 

OPERATION 

$3610  -s-  $95  =  38,  shares  purchased 

38  shares  =  $3800 
$3800  x  .06  =  $228,  income 

21.  How  much  will  be  realized  from  investing  $10304  in 
8%  stock,  bought  at  9  If,  brokerage  i%? 

22.  What  income  will  a  man  receive  by  investing  $6920  in 
5%  stock,  at  108,  brokerage  £%? 

28.  Find  the  annual  income  from  an  investment  of  $9276  in 
7%  stock,  bought  at  96-J-,  brokerage  -J%. 

24.  Which  is  more  profitable,  and  how  much,  to  invest 
$8400  in  4£%  stock  at  80,  or  in  6^%  stock  at  120? 

25.  A  man  owning  40  shares  of  6%  preferred  stock  sold  the 
same  at  112,  and  invested  the  proceeds  in  mining  stock  at  64. 


STOCKS  AND    BONDS  261 

Was  his  yearly  income  increased  or  diminished,  and  how  much, 
if  the  mining  stock  paid  a  dividend  of  3£%? 

26.  How  many  shares  of  6%  stock  must  be  purchased  to 
secure  an  income  of  $810? 

27.  How  much  must  be  invested  in  6%  stock,  at'  107,  to 
secure  an  income  of  $810? 

28.  When  5%  stock  is  selling  at  115,  how  much  must  be 
invested  to  yield  an  income  of  $875,  brokerage  •£%? 

29.  What   sum  must  be  invested  in  4£%    stock,   at  97-J-, 
brokerage  -£%,  to  .produce  an  income  of  $1845? 

30.  If  5%  bank  stock  is  5%  below  par,  what  sum  must  be 
invested  to  obtain  an  income  of  $1800? 

31.  If  20  shares  of  stock  yield  a  dividend  of  $140,  what 
per  cent  income  does  the  stock  yield? 

32.  If  I  buy  6%   stock  at  120,  what  rate  of  income  will  I 
receive  on  my  investment? 

OPERATION 

1  share  yields  $6  income. 

1  share  costs  $120. 

$6  is  5%  of  $120. 

Hence  the  investment  yields  5%. 

33.  A  dividend  of  4£%  was  declared  on  stock  bought  at  80. 
What  rate  of  interest  was  received  on  the  investment? 

34.  What  rate  per  cent  on  the  investment  is  realized  from 
6%  stock  bought  at  84? 

35.  Which  is  more  profitable,  and  how  much  per  cent,  to 
buy  6%  stock  at  108,  or  8%  stock  at  125? 

36.  I  wish  to  buy  stock  that  pays  6%   dividend  so  that  I 
may  receive  8%   income  on  my  investment.     At  what  price 
should  I  purchase  the  stock? 

OPERATION 

$1  of  the  stock  yields  $.06  income. 
$.06  is  8%  of  what  sum? 

$.06  +  .08  =  $.75,  the  price  at  which  the  stock  should  be 
purchased. 

37.  What  must  be  paid  for  10%   stock  so  as  to  realize  7% 
income? 


262  MODERN    COMMERCIAL    ARITHMETIC 

38.  At  what  price  must  6%  stock  be  purchased  to  yield  an 
income  of  6£%? 

39.  At  what  rate  of  discount  must  I  buy  6%   stock  that  I 
may  receive  an  income  of  7%  on  my  investment? 

40.  What  premium  can  a  dealer  pay  for  7%  stock  and  derive 
an  income  of  6  %  ? 

Watered  Stock 

472.  Some  corporations  are  prohibited  by  law  from  declaring 
dividends  in  excess  of  a  certain  per  cent.     If  a  corporation  with 
a  capital  stock  of  $2000000  gains  $200000,  and  is  not  allowed 
to  declare  a  dividend  greater  than  8%,  what  will  the  directors 
of  the  corporation  do?      They  may  give  to  the  stockholders 
$500000  of  new  stock.     Then  they  can  declare  a  dividend  of 
8%   on  $2500000,  and  divide  the  $200000  among  the  stock- 
holders without  violating  the  law.     The  $500000  of  stock  cer- 
tificates issued  adds  no  value  to  the  corporation,  but  it  enables 
the  corporation  to  declare  dividends  on  a  $2500000  basis  instead 
of  a  $2000000  basis.     Stock  issued  simply  to  swell  the  capital 
stock  is  called  Watered  Stock. 

The  managers  of  a  corporation  may  issue  watered  stock 
when  they  wish  to  keep  the  public  in  ignorance  of  the  true  rate 
of  dividends. 

New  York  Stock  Exchange 

473,  The  principal  stock  exchange,  or  stock  market,  in 
America  is  in  New  York  City. 

Most  of  the  stock  bought  and  sold  at  the  exchange  is  dealt 
in  not  to  raise  money  or  to  invest  money,  but  to  make  money 
on  the  rise  and  fall  in  the  price  of  stocks.  Dealers  sell  stock 
with  the  expectation  that  the  price  will  fall.  They  buy  stock 
with  the  expectation  that  the  price  will  rise. 

Dealers  who  try  to  drive  the  price  of  stocks  up  by  buying 
are  called  "Bulls." 

Dealers  who  try  to  drive  the  price  of  stocks  down  by  selling 
are  called  "Bears." 


STOCKS  AND   BONDS  263 

Besides  stock  of  the  various  corporations,  corn,  wheat,  cot- 
ton, etc. ,  are  sold.  When  wheat  is  sold,  the  seller  agrees  to 
deliver  the  wheat  to  the  purchaser  within  a  certain  period  on 
demand,  hut  the  purchaser  seldom  demands,  the  wheat.  He 
either  sells  the  "wheat"  or  settles  for  it  at  the  market  price. 
A  dealer  may  sell  1000000  bushels  of  wheat  if  he  has  not  a 
kernel  of  the  grain,  but  if  the  purchasers  demand  the  wheat  he 
must  deliver  it,  and  will  have  to  buy  it  in  the  market.  If  those 
who  have  bought  the  wheat  in  the  exchange  have  also  bought 
up  the  real  wheat  in  the  market,  they  may  compel  the  sellers 
of  wheat  in  the  exchange  to  buy  it  at  a  high  price. 

There  are  various  schemes  for  sending  the  price  of  stocks 
up  or  down. 

Buying  on  a  Margin 

474.  Stock  brokers  often  buy  stocks  on  a  margin.  If  a 
broker  offers  to  buy  cotton  for  a  speculator,  on  a  margin  of 
10%,  he  means  that  he  will  put  in  90%  of  his  money  and  10% 
of  the  speculator's  money,  buy  stock,  and  hold  it  to  the  gain  or 
loss  of  the  speculator.  The  broker  charges  a  commission  for 
buying  or  selling  stock,  and  interest  on  the  money  he  puts  in 
for  the  speculator.  The  speculator  may  give  instructions  to  his 
broker  as  to  when  to  buy  and  sell  stock,  or  he  may  let  the 
broker  use  his  own  judgment.  If  the  stock  that  the  broker 
buys  advances  in  price,  he  may  sell  it  and  remit  to  the  specu- 
lator the  gain  from  the  sale,  less  the  commission  and  interest 
charges.  If  the  stock  that  the  broker  buys  falls  in  price,  he 
may  hold  it  for  a  time,  expecting  it  will  advance  again.  If  the 
stock  is  sold  at  a  loss,  the  loss  and  the  broker's  charges  are 
taken  out  of  the  "margin."  When  the  price  of  the  stock  falls 
so  low  that  there  is  danger  that  the  margin  may  not  cover  the 
loss,  the  broker  sells  the  stock  to  save  his  money  invested. 

EXAMPLE. — A  speculator  sent  $510  to  a  broker  to  be  invested 
in  stock,  on  a  10%  margin.  The  broker  bought  stock  at  102, 
and  12  days  later  sold  it  at  105,  brokerage  £%  in  each  case. 
What  was  the  speculator's  net  gain,  if  the  broker  charged  6  % 
interest? 


264  MODERN   COMMERCIAL   ARITHMETIC 

OPERATION 

$  510  -?•     .10  =  $5100,  amount  invested 
$5100  -i-    1.02  =  $5000,  par  value  of  stock 
$5000  x    1.05  =  $5250,  selling  price  of  stock 
$5250  -  $5100  =  $  150,  gain  on  stock 
$5000  x  %%      =  $6.25,  brokerage  for  buying 
$5000  x  |%      =  $6.25,  brokerage  for  selling 

Int.  on  $4596.25  for  12  da.  =  $9.19 

$150  -  ($6.25  +  $6.25  -f  $9.19  )  =  $128.31,  net  gain 


PROBLEMS 

1.  A  broker  received  $1500  to  invest  in  stocks,  on  a  margin 
of  10%.  He  bought  120  shares  of  stock  at  105,  held  it  15  days, 
and  sold  it  at  108.  If  the  broker  charged  -J%  for  both  buying 
and  selling,  and  8%  interest  on  his  money  invested,  what  was 
the  speculator's  gain? 

#.  A  broker  received  a  remittance  of  $1200  as  a  10%  mar- 
gin,  and  purchased  200  shares  of  stock  at  60.  19  days  later  he 
sold  the  stock  at  82.  If  the  broker  charged  -J%  for  buying  and 
selling,  and  6%  interest,  what  was  the  speculator's  gain? 

3.  A  broker  received  $2000  for  an  S%  marginal  investment. 
He  bought  300  shares  of  stock  at  83,  held  it  3  days,  and  sold  it 
at  94.     Find  the  broker's  profit,  commission  £%,  interest  6%. 

4.  A  speculator  sent  his  broker  $5000  as  a  10%  margin  for 
investment  in  bank  stock.      The  broker  invested  $50000  in 
stock  at  125.     The  same  day  the  stock  fell  to  113,  and  the 
broker  sold  out  to  save  his  investment.     What  did  the  specu- 
lator lose,  brokerage  -£%? 

BONDS 

475.  A  Bond  is  a  form  of  commercial  paper  which  obligates 
the  person,  corporation,  or  government  issuing  it  to  pay  a  cer- 
tain sum  as  specified  in  the  bond. 

476.  When  a  corporation  or  a  government  wishes  to  raise  a 
large  sum  of  money  it  usually  prepares  and  sells  its  bonds. 
Such  bonds  bear  interest  payable  at  stated  times. 


STOCKS    AND    BONDS  265 

477.  Bonds  which  are  recorded  as  being  owned  by  and 
payable  to  certain  parties  are  called  Kegistered  Bonds. 

478.  Bonds  which  have  interest  certificates  attached  pay- 
able to  the  bearer  are  called  Coupon  Bonds. 

The  coupons  are  cut  off  and  presented  for  payment  when 
the  interest  is  due. 

479.  Government  bonds  are  often  described  by  abbrevia- 
tions.    "U.  S.  4's,  1907,  reg."  means  United  States  registered 
bonds,  bearing  4%  interest,  payable  in  1907.      "6's  coup." 
means  6  %  coupon  bonds. 

480.  Bonds,  like  stocks,  are  bought  and  sold  at  the  stock 
exchanges.     The  income  from  bonds  is   a  fixed   per  cent  of 
their  par  value,  while  the  income  from  stocks  depends  upon  the 
business  of  the  corporations  issuing  them. 


TAXES 

481.  A  Tax  is  a  sum  of  money  levied  by  a  government  on 
a  person,  his  property,  his  income,  or  his  business. 

482.  In  the  country  districts  of  some  States  a  tax  is  levied 
on  each  legal  voter,  for  the  support  of  the  public  roads.     This 
tax  is  called  a  Poll  Tax. 

483.  Taxes  are  levied  for  the  support  of  schools  and  for 
the  town,  county,  city,  and  State  governments.     Such  taxes 
are  levied  on  property. 

484.  Property  may  be  classed    as  real  property,  or  real 
estate,  and  personal  property.     Eeal  estate  consists  of  land  and 
buildings.      Movable   property,  live  stock,  money,  furniture, 
merchandise,  etc.,  is  personal  property. 

485.  Public  property  and  property  belonging  to  certain 
religious  and  benevolent  societies   are  e.xempt  from  taxation. 
The  law  sometimes  exempts  a  certain  amount  of  the  personal 
property  of  an  individual  from  taxation. 

486.  A  property  tax  is  levied  as  a  per  cent  on  the  property 
taxed.     It  is  usually  stated  as  so  many  mills  on  the  dollar. 
The  amount  of  tax  levied  on  $1,  expressed  decimally,  is  called 
the  Tax  Rate. 

The  value  of  the  taxable  property  in  a  city  is  $1612000,  and 
the  whole  amount  of  tax  to  be  raised  is  $9672.  The  tax  is 
what  per  cent  of  the  property?  What  is  the  tax  rate?  What 
is  the  tax  on  $1?  How  much  tax  will  a  man  have  to  pay  who 
is  assessed  (taxed  for)  $2635? 

The  value  of  the  property  taxed  is  what  element  in  per- 
centage? 

The  amount  of  tax  levied  is  what  element  in  percentage? 

The  rate  of  tax  is  what  element  in  percentage? 

487.  Officers  who  estimate  the  taxable  value  of  each  person's 
property  are  called  Assessors. 

488.  A  list  of  the  persons  taxed  with  tLe  assessed  value  of 
their  property  is  an  Assessment  Roll. 


TAXES 


267 


489.  Officers  who  collect  the  tax   are  called  Collectors. 
Some  collectors  receive  a  salary,  others  receive  as  a  fee  a  per- 
centage on  the  money  collected. 

PROBLEMS 

1.  In  a  city  in  which  the  tax  rate  is  .008,  Mr.  Wilson  owns 
real  estate  assessed  at  $6500  and  personal  property  assessed  at 
$3800.     What  is  the  amount  of  his  tax? 

2.  A  man  having  property  valued  at  $34750  is  taxed  at  the 
rate  of  f  %.     Find  the  amount  of  his  tax. 

3.  The  total  taxahle  property  in  a  village  is  assessed  at 
$2500000,  and  the  total  amount  of  tax  to  be  raised  is  $18500. 
The  tax  is  what  decimal  part  of  the  property?     What  is  the  tax 
rate?     Find  the  amount  of  tax  on  an  assessment  of  $2980;  of 
$36870. 

490.  Suppose  a  tax  of  $36495  is  to  be  levied  on  property 
assessed  at  $8117500.     There  are  about .  1500  taxpayers.     The 
process  of    finding   each  person's    tax    from  the  tax  rate,  as 
above,  is  too  long,  and  a  tax  table  is  used  to  shorten  the  work : 

TAX    TABLE 
Rate  .0045,  or  4}  mills  on  $1. 


Property 

Tax 

Property 

Tax 

Property 

Tax 

Property 

Tax 

$1 

$.0045 

$10 

$.045 

$100 

$  .45 

$1000 

$  4.50 

2 

.0090 

20 

.090 

200 

.90 

2000 

9.00 

3 

.0135 

30 

.135 

300 

1.35 

3000 

13.50 

4 

.0180 

40 

.180 

400 

1.80 

4000 

18.00 

5 

.0225 

50 

.225 

500 

2.25 

5000 

22.50 

6 

.0270 

60 

.270 

600 

2.70 

6000 

27.00 

7 

.0315 

70 

.315 

700 

3.15 

7000 

31.50 

8 

.0360 

80 

.360 

800 

3.60 

8000 

36.00 

9 

.0405 

90 

.405 

900 

4.05 

9000 

40.50 

In  finding  the  tax  on  $8745,  we  see  from  this  table  that  the 
tax  on 

$8000  =  $36.00 

700  =      3.15 

40  =        .18 

5=        .02 

$8745  =  $39.35 


268  MODERK   COMMERCIAL   ARITHMETIC 

PROBLEMS 

1.  From  this  table  find  the  tax  on  $46250,  $3928,  $60790, 
$1225,  $780,  $325,  $456,  $575,  $11690,  $5600,  $34750,  $23125. 

2.  The  assessment  roll  of  a  town  shows  that  the  total  tax- 
able property  is  assessed  at  $548000,  and  the  tax  to  be  levied  is 
$2904.40.     Find  the  tax  rate,  make  a  tax  table,  and  from  it 
find  the  tax  on  $12395,  $4560,  $7275,  $24890,  $43125. 

8.  Find  the  tax  on  the  following: 

Assessed  Valuation  Tax  Rate 

(a)  $4525  4    mills 

(»)       650  li  % 

(c)  1475  40^  per  $100 

(d)  2880  6    mills 

(e)  2590  %              25^  per  $100 

4»  In  a  village,  taxes  are  levied  as  follows:  For  street 
improvement,  $2100;  for  schools,  $7500;  for  salaries,  $2860; 
for  sinking  fund,  $3590.  The  valuation  of  the  property  is 
$2153800.  Find  the  tax  rate  to  five  decimal  places. 

5.  If  the  assessed  valuation  of  a  town  is  $985625,  what  tax 
rate  is  necessary  to  raise  $7950? 

6.  The  rate  of  tax  for  the  State  is  -§- %,  for  the  county  ^%, 
and  for  the  city  1  % .     Find  the  tax  on  city  property  assessed 
at  $3940. 

7.  A  man  owns  $12800  worth  of  property.     The  total  valua- 
tion of  his  school  district  is  $137500,  and  the  valuation  of  his 
town  is  $1426000.     The  expenses  of  the  school  are  $340,  and 
the  tax  levied  on  his  town  for  town,  county,  and  State  purposes 
is  $9450.     Find  the  whole  amount  of  tax  he  must  pay. 

8.  The  valuation  of  a  town  is  $975000.      The  amount  of 
tax  levied  for  town  expenses  is  $1240,  and  the  tax  rate  for 
county  and  State  purposes  is  4^  mills.      Find  the  total  tax 
levied  on  a  farm  worth  $3980. 

CUSTOM  HOUSE  BUSINESS 

491.  The  federal  government  derives  its  revenues  from 
indirect  taxation.  It  does  not  tax  the  property  of  an  indi- 


TAXES  269 

vidual,  but  it  puts  a  tax  on  some  things  that  are  manufactured 
in  this  country  and  on  some  things  that  are  imported  into  this 
country  from  abroad.  The  taxes  that  the  manufacturers  of 
tobacco,  beer,  whisky,  oleomargarine,  etc.,  have  to  pay  are 
called  Internal  Revenue  Taxes.  The  taxes  that  importers  of 
iron,  wool,  boots,  etc.,  have  to  pay  are  called  Duties,  or  Cus- 
toms. 

492.  Duties,  or  customs,  are  collected  at  the  various  Cus- 
tom Houses,  which  are  offices  established  at  the  principal  ports. 

493.  Ports  that  have  a  custom  house  are  called  Ports  of 
Entry,  because  goods  on  which  duties  are  levied  may  be  entered 
there. 

494.  The  principal  officer  in  charge  of  a  custom  house  is 
called  the  Collector  of  the  Port. 

495.  Duties,  or  customs,  are  levied  as  so  much  per  cent  on 
the  value  of  the  goods  imported,  or  as  so  much  per  pound, 
gallon,  bushel,  etc.,  without  regard  to  the  value  of  the  goods. 

496.  Duties  that  are  levied  as  a  per  cent  on  the  value  of 
the  goods  are  ad  valorem  duties. 

497.  Duties  that  are  levied  as  so  much  per  pound,  barrel, 
or  bushel,  are  specific  duties. 

498.  Ad  valorem  duties   are  levied  on  the  value  of  the 
goods  as  determined  by  the  prices  in  the  country  from  which 
they  are  imported. 

499.  The  ton  used  at  the  custom  house  is  the  long  ton  of 
2240  Ib. 

500.  On  some  goods  there  are  both  ad  valorem  and  specific 
duties. 

501.  A  Tariff  is  a  classification  of  goods  with  the  rates  of 
duty  imposed. 

By  the  tariff  act  of  1897,  the  duty  on  books  was  25%  ;  on 
certain  carpets,  28^  per  square  yard,  and  40%  of  their  value; 
on  onions,  40^  per  bushel;  on  cigars,  $4.50  per  pound  and  25% 
of  their  value. 

Which  of  these  articles  paid  ad  valorem  duties?  Which 
specific  duties? 


270  MODERN    COMMERCIAL   ARITHMETIC 

502.  On  some  goods  there  are  no  duties.     Such  goods  are 
said  to  be  on  the  Free  List. 

503.  Tonnage  is  a  tax  levied  on  a  vessel  for  coming  into  a 
port  of  entry. 

504.  Bringing  in  goods  by  stealth  so  as  to  avoid  paying  the 
duties  is  called  Smuggling.     It  is  a  crime  against  the  United 

States. 

505.  The  government  has  established  bonded  warehouses 
in  which  goods  may  be  stored  until  the  duties  have  been  paid. 

506.  In  estimating  the  duty  on  imported  goods  certain 
allowances  are  made.     Tare  is  an  allowance  made  for  the  weight 
of  the  box  or  other  covering  of  the  goods.     Breakage  is  an 
allowance  for  the  loss  of  liquids  in  bottles.      Leakage  is  an 
allowance  for  the  loss  of  liquids  in  .barrels. 


PROBLEMS 

In  the  following  examples  the  rates  of  duty  are  those  estab- 
lished by  the  tariff  act  of  1897. 

1.  Find  the  total  duty  on  2460  bu.  of  barley,  at  30^  per 
bushel;  680  Ib.  of  butter,  at  6^  per  pound;  475  Ib.  of  hops,  at 
12^  per  pound. 

2.  What  is  the  duty  on  an  invoice  of  blankets  valued  at 
$288,  and  weighing  640  Ib.,  if  the  tariff  rate  is  33^  per  pound 
and  35%  ad  valorem? 

3.  Find  the  duty,  at  60%  ad  valorem,  on  $6380  worth  of 
silk  lace. 

4.  Find  the  duty,  at  40^  per  gallon,  on  165  gal.  of  olive  oil. 

5.  Find  the  duty,  at  44^  per  pound,  and  50%  ad  valorem, 
on  14780  Ib.  of  knit  woolen  goods,  valued  at  25^  per  pound. 

6.  What  is  the  duty,  at  6^  per  square  yard,  on  3145  yd.  of 
rattan  matting? 

7.  What  is  the  duty,  at  1^  per  pound,  on  5370  Ib.  of  cas- 
tile  soap? 


TAXES  271 

8.  Find  the  duty,  at  40%  ad  valorem,  on  an  importation  of 
$38700  worth  of  watches. 

9.  What  is  the  duty,  at  38-J-0  per  pound  and  40%  ad  valorem, 
OD  1272  Ib.  of  woolen  yarn,  valued  at  33J#  per  pound? 

10.  What  is  the  duty,  at  600  per  square  yard  and  40%  ad 
valorem,  on  420  yd.  of  velvet  carpet,  valued  at  $3.50  per  yard? 


MISCELLANEOUS  REVIEW  PROBLEMS 

1.  52  men  working  8  hr.  per  day  can  do  a  piece  of  work  in 
28  da.     If  40  men  have  been  working  10  hr.  a  day  for  14  da., 
how  many  more  men  working  9  hr.  a  day    can  complete  the 
work  in  14  da.? 

2.  How  many  tons  of  coal  may  be  contained  in  a  bin  10  ft. 
square  and  6  ft.  high,  coal  weighing  80  Ib.  to  the  bushel? 

3.  A  wagon  box  12  ft.  6  in.  long,  3  ft.  4  in.  wide,  and  1  ft. 
9  in.  deep  is  full  of  wheat.     How  much  does  the  wheat  weigh? 

4.  Find  the  weight  of  a  bin  of  potatoes,  the  bin  being  8  ft. 
by  14  ft.  by  6  ft. 

5.  "What  is  the  cost  of  2942  Ib.  of  hay  at  $22.50  per  ton? 

6.  Write  ^  of  a  mile  in  lower  denominations. 

7.  The  drive  wheels  of  a  locomotive  are  5  ft.   10  in.  in 
diameter.     If  the  engine  runs  60  mi.  per  hour,  how  many  revo- 
lutions will  the  wheel  make  per  second? 

8.  Find  the  capacity  of  a  cylindrical  cistern  6£  ft.  in  diam- 
eter and  7  ft.  deep. 

9.  What  is  the  value  of  a  lot  198  ft.  long  and  176  ft.  wide 
at  $1250  per  acre? 

10.  Find  the  cost,  at  $14.75  per  M,  of  a  5-ft.  walk  around 
a  block  112  ft.  by  216  ft.,  the  walk  to  be  of  2-in.  plank  and  to 
rest  on  2  stringers  running  lengthwise,  2  in.  by  6  in.  each,  and 
placed  3  inches  from  each  edge. 

11.  A  man  receives  $3460  dividends  on  an  investment  of 
$40700.     What  is  the  per  cent  of  profit? 

12.  How  many  square  feet  of  sheet  iron  will  be  used  in 
making  a  7 -in.  stovepipe  of  40  joints  each  30  in.  long,  allowing 
1  in.  for  riveting? 

IS.  If  the  diameter  of  the  earth  is  7912  miles,  what  is  its 
circumference? 

14.  Find  the  weight  of  water,  at  62|  Ib.  per  cubic  foot,  in  a 
tank  22  ft.  in  diameter  and  18  ft.  high. 

273 


MISCELLANEOUS   REVIEW   PROBLEMS  273 

15.  Find  the  cost  of  a  stone  dam  80  ft.  long,  21  ft.  high, 
15  ft.  wide  at  the  base,  and  7  ft.  wide  at  the  top,  at  $2  per 
cubic  yard. 

16.  The  diagonal  of  a  square  lot  is  48  rd.     Eind  the  length 
of  a  side  of  the  lot. 

17.  What  distance  can  be  saved  by  going  diagonally  across  a 
lot  110  rd.  long  and  56  rd.  wide? 

18.  The  area  of  a  circular  lot  is  £  of  an  acre.     What  is  its 
diameter? 

19.  What  is  the  largest  square  that  can  be  cut  out  of  a  cir- 
cular board  20  in.  in  diameter? 

20.  A  man  receives  $250  per  month  rent  for  a  lot.     At  7% 
per  annum,  what  is  the  capitalization,  or  value,  of  the  lot? 

21.  May  29,  1902,  I  bought  a  house  for  $2600  on  6  mo. 
time  and  sold  it  Aug.  1,   1902,  on  8  mo.  credit  for  $3200. 
What  was  my  gain  per  cent,  money  being  worth  6%? 

22.  A  man  owned  a  house  which  rented  for  $50  per  month. 
His  insurance  and  taxes  amounted  to  $125  per  year,  and  the 
repairs  to  $50  per  year.      He  sold  the  house  for  $7000  and 
invested  the  money  in  6%  bonds  at  87,  brokerage  -J-%.     How 
much  was  tis  annual  income  increased  or  diminished? 

23.  What  is  the  present  worth  of  a  debt  of  $1268.40,  due  in 
1  yr.  7  mo.  12  da.,  money  being  worth  5$?? 

24.  A  boy  was  born  June  2,  1902.     What  sum   must  be 
placed  at    compound  interest   at  4%,  on  Dec.  25,   1902,  to 
amount  to  $10000  when  he  becomes  of  age? 

25.  A  dealer  sent  his  agent  $1740  to  invest  in  cheese  at  11^ 
per  pound.     If  the  commission  is  2-J-%  and  charges  $45,  how 
many  pounds  of  cheese  will  the  dealer  receive? 

26.  A  loaned  B  $6000  for  1  yr.  4  mo.  when  interest  was 
7%.      For  how  long  should  B  loan  A  $4000  when  interest 
is5%? 

27.  If  a  bicycle  wheel  is  28  in.  in  diameter,  how  many  revo- 
lutions will  it  make  in  going  1  mi.? 

28.  On  Jan.  1,  I  began  business  with  $8700  cash.     Since 
then  I  have  received  for  merchandise  $3625  in  cash,  have  $6490 
worth  of  goods  on  hand,  have  paid  $1750  in  wages,  and  $124- 


274 


MODERN   COMMERCIAL   ARITHMETIC 


for  expenses.  I  owe  bills  to  the  amount  of  $400  due  in  8  mo., 
without  interest,  and  am  the  creditor  of  bills  for  $1260  due  in 
6  mo.,  without  interest.  What  has  been  my  net  gain  per  cent 
to  date,  Dec.  1,  1902,  money  worth  6%? 

29.  From  the  following  data  show  the  gain  or  loss  and  the 
present  worth  of  the  business : 


Ledger  ] 

Too  tings 

Dr 

Or. 

Proprietor.  .            

$  8000 

Cash  

§12460 

10175 

Merchandise  

16520 

14240 

Bills  payable  

2000 

2400 

Bills  receivable    

2462 

400 

James  Robinson  

1180 

747 

\Villiam  Brown  

1498 

158 

Merchandise  on  hand  amounts  to  14685. 

SO.  April  3, 1902, 1  sold  James  Rice  merchandise  amounting 
to  $34.25,  and  took  his  note  at  2  mo.  without  interest.  Write 
the  note.  Find  the  proceeds  if  discounted  June  2, 1902,  at  6 %. 

31.  What  is  the  present  value,  June  16,  1903,  of  a  promis- 
sory note  for  $500,  dated  Jan.  1,  1903,  payable  one  year  after 
date  and  bearing  interest  at  6%? 

S2.  A  note  for  $800,  dated  Jan.  6,  1896,  bears  interest  at 
5%.  The  following  payments  have  been  made  on  it:  June  1, 
1896,  $15;  Sept.  1,  1896,  $40;  Jan.  5,  1897,  $150.  How 
much  remained  due  June  16,  1897? 

SS.  Find  the  equated  time  of  payment  of  the  following 
account : 


DR. 


WM.  JONES. 


CR. 


1900 

1900 

May 

5 

Mdse.,  at  30  da., 

$150 

June 

10 

Cash, 

$100 

July 

1 

Mdse.  ,  at  10  da.  , 

60 

10 

Cash, 

40 

Sept. 

10 

Mdse.,  at  20  da.. 

80 

July 

15 

Cash, 

55 

Nov. 

2 

Mdse.,  at  30  da., 

50 

34.  A  merchant  in  New  York  City  owes  5260  francs  in 
Paris.  What  will  it  cost  to  remit  (a)  direct  to  Paris  at  5.15  fr. 
a  dollar,  (Z>)  through  London  at  4.89,  there  buying  exchange 
on  Paris  at  25.19  fr.  a  pound  sterling? 


MISCELLANEOUS   KEVIEW    PROBLEMS 


275 


85.  From  the  following  balances  determine  the  gains  and 
losses,  the  resources,  liabilities,  and  present  worth : 


Dr. 

Cr 

Proprietor  (investment)  

35000 

Merchandise  

$8250 

6480 

Cash  

9560 

7845 

Bills  receivable  

1550 

Bills  payable  

780 

880 

James  Hill  .  .  .•  .  

425 

150 

Wheeler  &  Wilson  

630 

840 

Merchandise  on  hand  per  inventory,  $4125. 

86.  A  certain  stock  pays  10%.     At  what  rate  must  it  be 
bought  to  yield  6  %  on  the  investment? 

87.  What  single  discount  is  equivalent  to  a  trade  discount 
of  10,  15,  and5%? 

88.  What  premium  must  be  paid  to  insure  a  cargo  of   4880 
bu.  of  wheat,  valued  at  $1.04  per  bushel,  at  l-J-%,  the  policy 
being  for  only  f  of  the  value? 

89.  Find  the  cost  of  oil  cloth  for  a  hall  8f  yd.  long  and 
14  ft.  wide,  at  90^  a  square  yard. 

40.  Find  the  interest  on  $820.45  from  June  17,  1889,  to 
April  13,  1892,  at  4%. 

41.  4-ft.  wood  piled  5-J-  ft.  high  requires  how  many  feet  in 
length  of  the  pile  for  2-J-  cords? 

42.  Eeduce  3|%  to  a  decimal. 

48.  A  room  18  ft.  by  16  ft.  is  carpeted  with  carpet  f  of  a 
yard  wide,  and  the  smallest  possible  number  of  yards  of  the 
carpet  is  used.  Find  (a)  the  number  of  breadths;  (b)  the 
number  of  yards. 

44'  What  sum  will  amount  to  $354.09  in  7  mo.  at  3%  per 
annum? 

45.  How  many  brick  in  a  pile  16  ft.  by  6  ft.  by  4  ft.,  each 
brick  being  8  in.  by  4  in.  by  2  in.? 

46.  Eequired  the  exact  interest  on  $146.73,  for  23  da.,  at 
5  %  per  annum. 


276  MODERN    COMMERCIAL    ARITHMETIC 

47.  A  note  of  $285,  bearing  6%   interest,  given  June  17, 
1891,  has  endorsed  upon  it  a  payment  of  $100,  March  4,  1892. 
Find  the  sum  due  on  the  note  Nov,  1,  1892. 

48.  If  a  grocer  sells  coffee  that  costs  him  26-J-0  per  pound  and 
32^  a  hundred  for  freight,  for  36^  per  pound,  what  is  the  gain 
per  cent? 

4-9.  If  the  average  yield  per  bushel  of  seed  is  14  bu.  1  pk., 
how  much  is  the  yield  from  7  bu.  3  pk.  2  qt.? 

50.  Find  the  loss  on  26  shares  of  stock  bought  at  101,  and 
sold  at  87,  brokerage  -J-%  both  for  buying  and  selling. 

51.  Eequired  the  cost  of  24  3-in.  planks,  18  ft.  long  and 
10  in.  wide,  and  35  pieces  of  2  in.  by  4  in.  scantling  18  ft. 
long,  at  $20  per  M. 

52.  A  commission  merchant  sold  2140  bu.  of  oats  at  39^ 
per  bushel,  paid  $47.60  freight,  and  retained  2£%  commission. 
How  much  did  he  remit  to  the  consignor? 

53.  What  is  the  difference  in  weight,  expressed  in  avoirdu- 
pois pounds,  between  300  Ib.  Troy  and  300  Ib.  avoirdupois? 

54.  An  importer  receives  a  bill  of  goods  of  $575,  pays  a 
duty  of  45%,  and  sells  them  at  a  gain  of  20%.     The  price  paid 
by  the  purchaser  is  what  per  cent  of  the  exporter's  price? 

55.  A  man  bought  a  house  for  $4200,  paid  $640  for  repairs, 
and  rents  the  place  for  $50  per  month.     If  he  pays  $115  taxes, 
what  is  the  per  cent  of  income? 

56.  If  a  merchant  marks  goods  50%  above  cost,  what  dis- 
count from  the  marked  price  can  he  give  a  customer  and  make 
a  profit  of  33£%? 

57.  If  6%  bonds  are  selling  at  87,  how  much  money  must 
be  invested  in  them  to  secure  an  annual  income  of  $750? 

58.  An  agent  has  $23150  of  his  principal's  money  and  is 
instructed  to  buy  oats  at  48^  per  bushel,  with  a  commission  of 
5%.     How  many  bushels  should  he  buy? 

59.  When  N.  Y.  C.  4^'s  are  at  a  premium  of  H^-%,  what 
sum  must  I  invest  to  secure  an  income  of  $720? 

60.  I  bought  a  house  for  $750,  and  2  yr.  9  mo.  afterwards 
sold  it  for  $900.     If  I  paid  taxes  amounting  to  $29.17,  what 
was  the  annual  rate  per  cent  of  gain  on  the  money  invested? 


MISCELLANEOUS    REVIEW    PROBLEMS  277 

61.  How  many  feet  of  lumber  are  required  to  make  a  box 
4  ft  8  in.  by  3  ft.  6  in.  by  2  ft.  4  in.? 

62.  If  there  is  a  duty  of  $1.25  per  gallon,  and  45%,  on  var- 
nish, at  what  price  must  it  be  sold  per  gallon  to  gain  33£%,  if 
the  cost  in  London  is  $2.11  per  gallon  and  there  are  no  freight 
charges? 

68.  If  bell  metal  is  composed  of  78  parts  copper  and  22 
parts  tin,  what  weight  of  each  of  these  metals  will  there  be  in  a 
bell  that  weighs  900  lb.? 

64.  A  lot  60  ft.  by  150  ft.  was  sold  for  $500.     What  was 
the  price  per  acre? 

65.  If  the  water  from  a  spring  yields  Q^%  of  its  weight  in 
salt,  how  many  tons  of  water  will  be  required  to  make  1000 
lb.  of  salt? 

66.  What  is  the  rate  of  income  on  an  investment  in  5  % 
bonds  at  80%? 

67.  What  is  the  cost  of  3130  lb.  of  coal  at  $5.25  per  ton, 
and  1820  lb.  at  $6.90  per  ton? 

68.  If  your  standing  in  attendance  at  school  is  marked  88  % 
and  you  were  absent  9  da.,  how  many  days  of  school   were 
there? 

69.  Find  the  proceeds  of  an  interest  bearing  note  for  $186 
given  for  3  mo.  and  discounted  the  same  day  it  was  made, 
interest  and  discount  being  6%  each. 

70.  If  a  man  bought  stock  at  2%  above  par,  and  sold  it  at 
7%  below  par,  what  per  cent  did  he  lose? 

71.  The  valuation  of   the  taxable   property  of  a  town  is 
$498700  and  the  tax  to  be  raised  is  $5850.     What  will  be  the 
tax  on  $5000? 

72.  I  bought  shoes  at  $2.40  per  pair.     At  what  price  must 
I  mark  them  that  I  may  allow  a  discount  of  25%  and  make  a 
profit  of  20%? 

78.  A  man  bought  a  lot  for  $400  on  these  terms:  $100  cash 
and  the  balance  in  monthly  installments  of  $20,  with  6%  interest 
on  the  part  unpaid,  interest  payable  with  every  installment. 
What  was  the  total  amount  paid  for  the  lot? 

74>  Four  men  formed  a  partnership.     A  put  in  $12800,  B 


278  MODERN    COMMERCIAL   ARITHMETIC 

put  in  $14000,  C  put  in  $11900,  and  D  put  in  $15000.     After 

9  mo.  A  drew  $2800,  and  10  mo.  later  put  in  $4600.     After  10 
mo.  B  added  to  his  investment  $5200,  and  C  withdrew  $6100. 
They  paid  $8425  for  labor,  $1750  for  repairs,  $1450  taxes.     In 
2  yr.  they  were  worth  $68000.     What  was  each  partner  worth? 

75.  I  bought,  through  an  agent,  5000  bu.  of  corn  at  580, 
commission  2%.     The  agent  sold  the  corn  at  640,  commission 
2|%,   charges  $42.50,   and   remitted  the  balance  by  a  draft 
purchased  at  f  %  premium.     What  was  my  gain? 

76.  A   man   bought   goods    for    $2560.      He  paid  $21.50 
insurance,  $75.50  cartage,  and  sold  them  for  $2975,  allowing  the 
agent  a  commission  of  4%  for  selling  the  goods.     What  was 
the  gain  per  cent? 

77.  In  writing  on  the  typewriter  the  letter  a  was  struck 
33520  times,  b  13080  times,  e  25160  times,  c  15260  times,  and 
j  2180  times.     What  was  the  per  cent  of  use  of  each  letter? 

78.  A  grocer  has  teas  worth  140,  180,  250,  320  per  pound. 
In  what  proportions  can  he  mix  them  so  as  to  make  the  mix- 
ture worth  220  per  pound?     How  many  pounds  of  the  mixture 
must  he  make  to  use  up  125  Ib.  of  the  180  tea? 

79.  A  dealer  bought  300  casks  of  vinegar,  each  containing 
45  gal.,  at  100  per  gallon.     He  paid  $1  apiece  for  the  barrels, 

10  per  gallon  freight,  100  per  barrel  cartage.     He  sold  it  at 
12^0  per  gallon,  receiving  900  for  each  barrel,  and  paying  7|% 
commission  for  selling.     What  was  his  total  gain? 

80.  On  the  following  note  these  payments  were  made :  Feb. 
11,  1902,  $240;  March  18,  1902,  $375;  May  20,  1902,  $260: 

$1500.00.  Chicago,  111.,  Jan.  2,  1902. 

Six  months  after  date,  for  value  received,  I  promise 
to  pay  J.  K.  Welsh,  or  order,  fifteen  hundred  dollars, 
with  interest  at  6  per  cent. 

THOMAS  H.  BEAMAN. 

What  was  due  on  the  note  Dec.  24,  1902? 


ANSWERS 


Art.  17,  p.  13 

8.  10343279 

Art.  81,  p,  24 

1.  44782 

9.  8605464 

1.  2207 

2.  488943 

10.  8179692 

&  4883 

S.  4201420 

11.  9083787 

J.  716 

4.  4309104 

12.  10170524 

4.  932 

5.  3882493 

IS.  8638249 

5.  6178 

6.  384929783 

14.  9632366 

6.  470597 

7.  397334694 

15.  11443360 

7.  242202 

8.  406274798 

16.  8627036 

5.  89787 

9.  423007285 

17.  10084434 

9.  222071 

10.  445609793 

18.  9816995 

10.  293253 

11.  549333911 

19.  10046349 

11.  14722007 

12.  446378793 

20.  10647803 

12.  3049258 

IS.  659402301 

21.  10755906 

15.  15812417 

14.  878654438 

U.  2329188 

15.  781811566 

Art.  30,  p.  22 

15.  1835007 

16.  766652422 

16.  7175118 

1.  643 

17.  808479253 
18.  901317663 
19.  690428361 

2.  4016 
3.  3545 

Art.  34,  p.  25 

1.  1480 

20.  8238138 

4.  33243 

&  688 

21.  7774858 
22.  7547458 

5.  15211 
6.  29312 

3.  5156 
4.  76628 

23.  9165011 

7.  23811 

5.  17472 

24.  8615227 

*.  20680 

6.  63087 

25.  8725835 

9.  30765 

7.  4100 

26.  7131512 
27.  9288411 

10.  186999 
11.  145408 
12.  102527 

8.  23303 
P.  18366 
10.  64369 

Art.  22,  p.  18 

15.  87099 

11.  7459 

1.  9147136 

14.  48641 

12.  11401.34 

2.  7422902 

15.  17034 

13.  §6871.45 

3.  9934025 

16.  26682 

14.  §9434.93 

4.  8722928 

17.  20322 

15.  14667.20 

5.  8988061 

IS.  26428 

16.  §45360.45 

6.  7391684 

19.  90314 

17.  §116104.28 

7.  7553772 

m  115853 

18.  §140.73 

379 

880 


AtfSWEBS 


19.  $861.11 

J.  2666 

4.  42756 

go.  $13196.43 

4.  2044 

5.  257796 

Art.  37,  PC  27 

5.  6392 
6.  3922 

ft  126468 

7.  68962 

1.  183 

7.  3886 

S.  120411 

S.  210 

S.  3420 

9.  4503 

5.  195 

9.  2668 

10.  125944 

4.  240 

10.  1015 

11.  196315 

5.  221 

11.  1702 

12.  25245 

ft  247 

12.  2544 

13.  16536 

7.  238 

15.  1950 

14-  125008 

o  oon 

o.  £  l\) 

U.  3901 

15.  50996 

9.  304 

15.  5952 

16.  633825 

10.  306 
11.  285 

16.  3293 
17.  3404 

Art.  44, 

p.  31 

10.  288 

IS.  3496 

1.  198 

15.  361 

19.  4898 

0.  286 

14.  252 

$0.  6072 

3.  1485 

15.  255 

£  836 

16.  238 

Art.  42,  p.  30 

5.  3465 

17.  216 

1.  5382 

ft  2706 

IS.  342 

g.  14484 

7.  7909 

Art.  39,  p.  28 

5.  21546 
4.  42490 

8.  2893 
P.  3916 

1.  35100 

5.  180852 

10.  10373 

g.  8432000 

ft  394632 

11.  2827 

3.  712400000 

7.  77868 

lg.  7095 

4.  46800000 

S.  323228 

15.  14982 

6.  1736000 

9.  95988 

14.  27280 

ft  56000000 

10.  141245 

15.  78716 

Art.  40,  p.  29 

11.  124323 

1ft  33682 

1.  86625 
g.  6019936 

n.  2313396 
15.  1783800 

Art.  47, 

p.  33 

3.  56939 

14.  3382260 

1.  327 

4.  6774792 

15.  1878874 

0.  444(8rem.) 

5.  3059625 

16.  484956 

3.  538 

6.  74664 

17.  351663 

4.  144 

7.  867456 

18.  5344924 

5.  4739 

8.  217665 

19.  4591947 

6.  43785  (1 

rem.) 

9.  359074 

gO.  649540 

7.  21318 

/0.  271466 

Art.  43,  p.  31 

8.  317 
5.  327 

Art.  41,  p.  30 

1.  3068 

10.  514 

1.  1428 

g.  6608 

11.  1006 

g.  1481 

5.  21046 

12.  428 

AHSWERS 


281 


IS.  9512 

7.  lift 

14.  11080  (398  rem.) 

8-  1TW 

15.  3323  (715  rem.) 

16.  1921  (1771  rem.) 

_20  2-jY^r 

17.  208  (1846  rem.) 

11.  20 

18.  63  (7323  rem.) 

12.  70 

19.  647  (2983  rem.) 

15.  $6 

gO.  1139  (652  rem.) 

14.  117 

Art.  48,  p.  33 

15.  255f 

1.  468 

'  Il3^33 

g.  73 

15.  12| 

3.  28  (60  rem.) 

19.  40 

4*  79  (6800  rem.) 

5.  63  (875  rem.) 

gl.  70 

ft  420  (70  rem.) 

22.  3402 

7.  537  (31936  rem.) 

25.  15 

8.  80016  (7829  rem.) 
9.  670  (197356  rem.) 

24.  144TV 

10.  5179  (36527  rem.) 

si 

Art.  54,  p.  36 

Art.  73,  p.  46 

1.  $160 

1.  25.6 

g.  A  =  90 

2.  425.54 

3.  $24 

5.  659.656 

4.  A  =  24 

4.  1797.90311 

5.  $30 

5.  1112.928 

[6.  $75 

6.  1610.9902 

1  7.  $70 
8.  $25 

7.  329.9351 
ft  260.53739 

9.  $60 

10.  $40 

Art.  74,  p.  46 

11.  $6 

1.  .706 

12.  A  =  25 

2.  7.8016 

IS.  4360 

5.  407.585 

1^.  751 

4.  206.9985 

15.  24 

5.  41.8017 

6.  3158.1015 

Art.  58,  p.  38 

7.  902.8887 

1.  22f 

ft  16360.4852 

*.  2730| 

S.  40j 

Art.  75,  p.  47 

4-  3T2T6/A 

1.  1.162 

£.  2j-  j- 

2.  .4025 

ft  1ft 

5.  .022032 

4.  .0960 

5.  .0001537 
ft  .000320608 
7.  .0150294 
ft  .0279 

9.  3.385 

10.  .08891 

11.  10000 

12.  .01 

13.  .0001001 

14.  .0000001 

15.  .00010001 

16.  1 

17.  10011.0011001 

18.  100000001 

19.  25025025 

20.  2500002.5025000025 

Art.  76,  p.  48 

1.  2.725 

2.  356^ 

3.  587.2 

4.  60000 

5.  .000052 

6.  .0000007 

7.  250000 
ft  .26| 

9.  5.0607 

10.  .156 

11.  .0135 

12.  2.143 

15.  .00009325 

14.  .144 

15.  .00000697 

16.  .10809 

17.  .007225 

18.  .000901 

19.  1,  100,  10,  10, 
10000,  .1,  100,  1, 
1,  .01 

SO.  .5,  .005,  .5,  .005, 
.0005,  50000, 
.0000005,  50000, 
50,  5000000 


282 


ANSWERS 


21.  .16,  1600,  .00016, 
1.6,  16000, 
160000000, 
.0000000016,  .0016, 
160000,  1.6 

22.  3,  .000003, 
30000000,  .03, 
30000,  .OOOC00003, 
.03,  300,  3000000, 
.00000000003 

23.  .02,  2000, 
200000000, 
.000000002,  .02, 
200,  .000000002, 
2000000000,  2000, 
.00002 

24.  .005  .00005, 
500000000,  5, 
.000000005,  .005, 
500,  50000000, 
.000000005,  .005 

Art.  7  7,  p.  49 


2.  .64 

S.  T*» 

4.  .8 

5.  .8 

6.  .25 


8. 

10.  jUh 

x  T!L 

13. 


17.  17TW<> 
18. 


O.    101TVoV 


22.  A 

23.  .625 

24.  .8 

25.  .75 

26.  .375 

27.  .5 

28.  .6 
£9.  .875 

50.  .1666+ 

51.  .555+ 

50.  .666+ 
33.  .5714+ 

54.  .1875 

55.  .5333+ 
36.  .15 

57.  .64 
55.  .35 

59.  .9166+ 

40.  .933+ 

41.  .6428+ 
40.  .8333+ 
45.  .09375 
44-  -032 

45.  .8875 

46.  .175 

47.  .248 

48.  .2733+ 

49.  .1666+ 

60.  .246 

51.  .24416+ 

50.  .96875 
53.  .184 
54-  7.125 

55.  17.0285+ 

56.  14.2857+ 

57.  20.0075 
55.  25.08 

59.  9.0583+ 

60.  16.005 

61.  5.00125 

Art.  78,  p.  50 

i.  V 
A  W 


5. 

4.   W 

J'   ffi 


11 
*0. 


Art.  79,  p.  51 


3.   V 


5. 


*    J&6 

*  W 

9.  W 

5  -w 

10.  W 

Art.  80,  p.  51 

1.  7j 

5.  15 

4.  47| 

5.  8f 
6. 


8.  13 

9.  19Jf 

10.  55 JB 

11.  341* 


Art.  81,  p.  51 

* 
I 

I 


ANSWERS  283 

s.  rYA,  TVA,          11.  I! 


12.   Iff 

»-t  •  I!!!!!' 5¥BJ4*'  "7. 

Art.  82,  p.  52  «•  ^A,  TWA>          W.  37i 

IS.  iVAVA,  Art.  96,  p.  57 


5.  T¥T 

e.  m  5.  4}J 

7.  TTS  Art.  90,  p.  54  6.  43 

s.  m  i  ^v  7.  5* 

9.  ft  J  rv  9.  it 

W.  Iff  .'  ,1 01  10.  8} 

w.  Hit  4  1 74^  a-r.  4 

».  T1^  5;  tin  «.  I 

Art.  88,  p.  53  6.  lH  "'  /7 

_j    24  7.  tiiii  ^-  6ia 


*.  144  8.  Ifji  "' 

S.  360  9.  6H  „'   V 

4.  84  ^  «'s^  18'  ^ 

5.  60  U 

6.  11088  IS.  42lHf  m   Jj1 

^.  42 


Art.  89,  p.  53  ^    °  |{f  M.  17H 

-       072       188^        7_S  "^"  3  3  6 

1.     II  $1     frfl»     8%  yr 

t»  16 

2.  in,  ui,  m, 

444-  #0    262 

5.  Ill  ift,  Aft,  Art*  91f  P*  65  ^-  189A 

1.  A  98.  189 

£.  J  29.  306jf 

5.  ify  50.  1309J 
5.  |M,  |jj,  i**,            4.  ^A  «•  6507 

iff  5.  A  W-  H568f 

6.  *VV  W-  1525A 

7.  2 1  54.  672| 
S.  H  55.  45895 


57.  1389 


284 

55.  4835 

39.  790 

40.  1220 

41.  445| 

42.  732 

43.  492 


45.  1113 

'40.  244f£ 

47.  5483if 

45.  4821  A 

42.  39971$ 

50.  904f 

51.  265011 
58.  228381H 

53.  41269/? 

54.  760f-f 

55.  381  f| 

56.  1146fj 

57.  2264T\ 


Art.  97,  p.  59 


i.  ' 


*.  A 

*  A 


e.  A 

7.  A 

*  A 

9.  A 

10.  A 


15.  l 

j*.  H 


17. 


.  J 

.  Mr 
.  ft 
•  A 


ANSWERS 
5.  276}$ 


^7.  6H 
98.  14T6! 


.  11221 


36.  4 
57.  li 

^.  n 

39. 

40. 
41. 


46. 


Art.  98,  p.  61 

1.  120 

*A 

5.  A 

4.  3li 

5.  49 
e.  24 
7.  547J 
5.  If 

«.  iiV 

m  135 

^-  A 


**•  fit 


15. 
^. 
17.  22H 


P.  T 
?.  1st, 
3d, 


;2d, 


Art.  100,  p.  64 

i.  llf  wk. 
^.  58.24bu. 
5.  .814|  mi. 

4-  A, 


5.  116H 

^.  $2.02 

7.  iieH 

^.  169.71 
P.  1000  Ib. 


Art.  Ill,  p.  68 

1.  91800,  45900, 
22950,  15300, 
11475 

2.  122400,  81600, 
61200,  40800, 
30600,  20400, 
15300 

3.  18400,  12266f  , 
9200,  6133^,  4600, 
3066f  ,  2300 

4.  140,  1400,  14000, 
105,  1050,  10500 

5.  140,  1400,  14000, 
70,  700,  7000 

6.  810,  8100,  81000, 
4050,  40500 

7.  157J,  1575, 
15750,  315,  3150, 
81500 


ANSWERS 


285 


8.  1300,  13000,  390, 
3900,  39000,  5200 

9.  1600,  16000,  2133}, 
21333},  6400, 
85333} 

10.  $1320,  $880,  $660, 
$440,  $330,  $220, 
$165 

11.  $61.33},  $460, 
$30.66f,  $230, 
$153.33},  $11.50 

12.  $16.80,  $11.20, 
$8.40,  $112,  $84, 
$5.60,  $42,  $4.20, 
$56,  $420,  $28, 
$210,  $280,  $21, 
$168,  $1120,  $840 
$560 

13.  $12.80,  $1920, 
$128,  $192,  $1280, 
$19.20,  $9.60, 
$2560,  $96,  $256, 
$960,  $25.60,  $64, 
$51.20,  $640,  $48 

14.  $660,  $66,  $880, 
$1320,  $88,  $132 
$176 

15.  $28800,  $192, 
$14.40,  $96,  $1920, 
$72,  $960,  $36, 
$36000,  $720 

Art.  115,  p.  73 

1.  $6.64 

2.  $38.98 

3.  $93.22 

4.  $164.52 

5.  $130 

6.  $6.88 

7.  $21.98 

8.  $10.83 

9.  $60.30 
10.  $111.34 


Art.  116,  p.  73 

7.  5  da.  16  hr.  2  min. 

1.  $17.79 

34  sec. 

2.  $82.92 

8.  9  sq.  yd.  8  sq.  ft. 

3.  $98.33 

47  sq.  in. 

4.  $49.49 

9.  23  Ib.  10  oz.  2  dr. 

5.  $20.05 

Isc. 

6.  $13.10 

10.  1  mi.  14  ch.  3  rd. 

7.  $54.94 

31. 

'*.  $1.68 

11.  215  rd.  4  yd.  1  ft. 

9  in. 

Art.  11  7,  p.  74: 

12.  6  bbl.  25  gal.  1  pt. 

1.  $23.47   7.  $22.31 

1  gi- 

2.  $26.06   A  $25.11 

13.  2  Ib.  6  oz.  5  dr. 

A  $11.71   9.  $24.11 

14.  7  mi.  67  ch.  3  rd. 

4.  $29.36  10.  $13.73 

9  1. 

5.  $31.20  11.  $132.41 

15.  5  sq.  yd.  3  sq.  ft. 

6.  $101.44  12.  $38.68 

40  sq.  in. 

IS.  $493.01 

16.  47  da.  17  hr.  54 

14.  Cost,  $6.22;  price, 
$5.50 

min. 
17.  10  Ib.  8  oz.  13  gr. 

15.  $7.17,  23c. 

18.  12  cu.  yd.  4  cu. 

1(5.  $18.28 

ft.  605  cu.  in. 

17.  Cost,  $6.91;  price, 

19.  24  bu.  3  pk.  4  qt. 

$6.25 

1  pt. 

18.  $41.81 

80.  46  Ib.  11  oz.  8 

19.  $72.77 

pwt. 

#0.  $38.98 

81.  1672  in. 

81.  2625  Ib. 

88.  17174ft. 

£0.  $10.03 

83.  16336  gr. 

2S.  $29.70 

84-  15460  sec. 

&#.  35c 

85.  8476  sc. 

25.  $82.67 

86.  3319  in. 

87.  4082  pwt. 

Art.  160,  p.  85 

28.  2906  min. 

1.  21  rd.  2}  yd.  8  in., 

29.  1321  sc. 

or,  21  rd.  2  yd.  2 

SO.  57620  sec. 

ft.  2  in. 

SI.  72920  sec. 

8.  Imi.  117  rd.  lyd. 

32.  191  gi. 

1  ft.  5  in. 

33.  955  pt. 

S.  10  bu.  2  pk.  6  qt. 

34.  166694  cu.  in. 

4-  39  gal.  3  qt. 

35.  165  pt. 

5.  2  oz.  14  pwt.  2  gr. 

36.  518  gi. 

(5.  2  Ib.  8  oz.  4  dr. 

37.  161  pt. 

2  sc.  12  gr. 

S8.  147  cu.  ft. 

286 


ANSWERS 


39.  466  gi. 

8.  120  sov.  8s.  3d.  3 

23.  4  gal.  1  qt.  1  pt. 

40.  698  dr. 

far 

1  gi. 

41.  6  ft.  7^  in. 

9.  162  sov.  16s.  7d. 

24.  167  bu.  1  pt. 

42.  35  rd.  9  ft.  2  in. 

3  far. 

25.  5  yr.  8  mo.  19  da. 

43.  14ft.  2.  28  in. 

20.  79  sov.  2d.  1  far. 

9  hr.  58  min. 

44-  4  oz.  10  pwt. 

22.  1325  sov.  7s.  9d. 

45.  3hr. 

1  far. 

Art.  163,  p.  90 

46.  9  oz.  2  sc.  17.6  gr. 

12.  120  sov.  9s.  4d. 

2.  2  yr.  9  mo.  7  da. 

47.  11  cu.  ft.  1404  cu 

2.  3  yr.  9  mo.  11  da. 

in. 

Art.  162,  p.  89 

3.  1  yr.  8  mo.  15  da. 

48.  2  pk.  1  qt.  if  pt. 
49.  3qt.  1  pt.  2.08  gi. 

2.  26  Ib.  4  oz.  7  pwt. 

4.  2  yr.  1  mo.  16  da. 
5.  3  yr.  3  mo.  16  da. 

50.  3  sq.  ft.  108  sq.  in. 
51.  3  qt.  1  pt. 

11  gr. 
2.  250  rd.  1  yd.  1  ft. 

6.  186  da. 
7.  93  da. 

52.  16  sq.  yd.  5  sq.  ft. 
106.  2  sq.  in. 

7  in. 
3.  103  gal.  3  qt. 

8.  98  da. 
9.  179  da. 

53.  j-$?  bu. 

4.  11  cu.  yd.   10  cu. 

20.  156  da. 

54.  .019375  gal. 

ft.  524  cu.  in. 
5.  1  Ib.  lloz.  13  pwt. 

Art.  164,  p.  91 

56.  sij  Ib. 

4gr. 

2.  37.236qt. 

57.  Tinnrlb. 

6.  7 

2.  \^  Ib. 

58,  .02074+  cu.  yd. 
S9.   j"4o  "o"o~  mi. 

7.  13 
8.  96  bu.  2  pk.  6  qt. 

3.  10  Ib.  7  oz.  12  pwt. 
2gr. 

60.  .0001475  Ib. 

9.  2    da.    20    hr.    29 

4.  1  Ib.  2  oz.  11  pwt0 

61.  -rJ-g-  gal- 

min.  24  sec. 

16  gr. 

6#.  TIT  o"ir  mi. 

20.  4    mi.    286    rd.    1 

5.  54  + 

63.  .0041b. 

yd.  1  ft.  2  in. 

6.   51yV 

64.  .003645  Ib. 

22.  1  bu.  2  pk.  3l  qt. 

7.  496  bu. 

65.  .  38611+  Ib. 
66.  .528125  da. 

13.  8  Ib.  3  dr.  14  gr. 

8.  137J  bu. 
9.  7iiy  gal. 

67.  .6875  gal. 

24.  42  da.  6  hr.  2  min. 

20.  2872f£  gal. 

68.  .64lf  sov. 
69.  .703125  bu. 

48  sec. 
25.  189  rd.  4  yd.  7  in. 

Art.  170,  p.  93 

70.  .727083jsov. 

26.  41 
27.  37  gal. 

2.  (a)  12X18,  24X9 

Art.  161,  p.  87 

18.  52  mi.  17  rd.  2  ft. 
2  in. 

(c)  14X21,  28xlO| 
(d)  16X22,  32X11 

1.  $124.07 

19.  8  mo.    26    da.    18 

4.  7X9J,  4§X14, 

2.  $398.25 

hr.  34  min.  32  sec. 

3^X21 

3.  $105.99 

20.  88  Ib.  5  oz.  4  pwt. 

5.  7X11,  5^X14 

4.  $82.43 

16  gr. 

6.  5^X8,  4X11, 

5.  $169.06 

21.  42   mi.   186  rd.   5 

2fxl6 

6.  $65.06 

yd.  2  ft.  3  in. 

7.  10fx5i,  4Xl4f, 

7.  31  sov.  7s.  Id.  3 

22.  89  A.  131  sq.   rd. 

8X7J,  5^X11, 

far 

27|  sq.  yd. 

16X3|,  2fx22 

ANSWERS 


287 


8.  5^X8,  4X11, 

part;  3d,  2  parts; 

Art.  188,  p.  103 

2fxl6,  2X22 
9.  Same  as  problem  4 
10.  7^X4,  2|X10|, 

4th,  4  parts 
3.  5.  2,  2,  20,  or  5,  4, 
4,  20,  or  5,  6,  6,  20 

1.  28$  sq.  yd. 
2.  10  A.  150  sq.  rd. 
3.  96  sq.  rd. 

See  problem  3, 

4.  3,  3,  3,  and  12  lb. 
respectively 
5.  lst,641b.;3d,81b. 
6.  240  lb.  at  40^,  240 

4.  283^  sq.  ft. 
5.  USAVrsq.  rd. 
(5.  17  A.  37ilf  sq.  rd. 
7.  6A. 

6ix6j,  4jx9^/ 

lb.  at  55^,  80  lb.  at 

8.  1512  sq.  ft. 

8^X5,  3|xl3£, 

65^,  400  lb.  at  75^, 
720  lb.  at  85^ 

9.  714  sq.  yd. 
10.  $14.85 

6ix6f,  4^X10, 

7.  5,  6,  and  5  parts 
respectively 

21.  5|  sq.  rd. 
12.  1638  sq.  ft. 

9jx5j,  3^X14, 

8.  10,  10,  10,  and  29 

15.  64{f  rd. 

7X7,  4f  XlOi 

parts  respectively 

14.  4736   sq.  in. 

14X3|,  2^X21, 
See  problem  7, 

9.  19  of  1st,  39  of  2d, 
285  of  3d,  25  of  4th 

15.  606|  sq.  yd. 

12X6,4^X16, 

P.  99 

Art.  189,  p.  105 

9X8,  6X12, 
18X4,  3X24, 

1.  $.8115 
2.  $1516.69 

2.  $2160 
3.  $5000 

123X63,  4jXl6?, 

3.  $44622.09 

4.  $2052 

93X83,  6^X12^, 

4.  130 

5.  $1400 

19X4S,316X25 

5.   $111.27 

6.  $10666f 

11.  8X4|,  3X12|, 

6.  33.75 

7.  $2666.67 

12X3L  2X19 

7.  197.21 

o     <flJQft7* 

8.  $18 

12.  There    are    no 

o.    «S>ov/  i  ti 

9.  98^ 

Art.  190,  p.  106 

sheets  in  the  table 
large  enough. 

10.  W,  ^  part 
11.  $72.30 

1.  128  rd. 
2.  151.4004  A. 

13.  22x32 
U.  25X40 

12.  $16.61 
13.  190.40 

3.  19yd. 
4.  $918 

15.  32X44 

14.  41.89  qt. 

5.  63T\  ft. 

Art.  172,  p.  96 

15.  6178.92  ft. 

6.  544  sq.  ft. 

16.  1608  lb. 

7.  10164  sq.  yd. 

1.  74i/ 

17.  2202.07  francs, 

8.   64  sq.  yd. 

2.  $.0341 

1781.97  marks 

9.  38|f  rd. 

3.  $.5996 

18.  $286.80 

10.  1144  sq.  ft. 

4.  $.704 

19.  $605.31 

5.  47Jc 

20.  $22.30 

Art.  192,  p.  108 

21.  $32.82 

1.  1152  sq.  ft. 

Art.  173,  p.  98 

22.  $.60 

2.  3180  sq.  yd. 

1.  50  lb.,  125  lb.,  50 

05.  23  bu.  3  pk.  7  qt. 

3.  2294  sq.  rd. 

lb.,  50  lb. 

84-  $407 

4.  7475  sq.  rd. 

2.  1st,  2  parts;   2d,  1 

25.  $11.20 

5.  3182  sq.  ft. 

288 


ANSWERS 


6.  15435  sq.  yd. 

7.  11684f  sq.  yd. 

8.  65ft. 

9.  19200  sq.  ft. 

10.  832J  sq.  ft. 

11.  21-rV  A. 
1*.  26f  rd. 

.13.  8|4  ft. 

14.  8  rd.,  6  rd.,  4|  rd. 

15.  203  sq.  rd. 

Art.  193,  p.  109 

1.  266  sq.  ft. 
S.  750  sq.  yd. 

3.  3755 1  sq.  yd. 

4.  118572  sq.  ft. 

5.  3801  sq.  rd. 

6.  20  rd. 

7.  14^V  A. 

A  600  sq.  rd. 

9.  $6776 

10.  7l|rd. 

Jl.  6»V  A. 

IS.  28j  sq.  ft. 

JW.  384  sq.  ft. 

U.  494  sq.  in. 

Art.  198,  p.  110 

1.  65  sq.  ft. 

S.  174  sq.  ft. 

3.  186ft  sq.  yd. 

4.  477.12sq.  ft. 

5.  93f  sq.  ft. 

6.  166.32  in. 

7.  7ift. 

8.  10.4ft. 

9.  43. 0119  sq.  ft. 

10.  1731. 197  sq.  yd. 

11.  21.217  sq.  ft. 
IS.  2519. 134  sq.  ft. 

13.  2992  sq.  ft. 

14.  3330.84  +  sq.  yd. 

15.  1236. 077  «q.  ft. 


Art.  203,  p.  112 

1.  87.96  ft. 
S.  15.597yd. 
3.  17.825  yd. 
4-  43.98ft. 

5.  10.822yd. 

6.  131.947ft. 

7.  15.119yd. 

8.  43.982rd. 

9.  39.152rd. 
10.  72.78ft 

Art.  205,  p.  113 

1.  198.9f  sq.  ft. 
S.  8148.48  sq.  rd. 

3.  286.478  sq.  ft. 

4.  17.104sq.  ft. 

5.  50.265  sq.  ft. 

6.  53.794  sq.  yd. 

7.  91. 987  sq.  yd. 

8.  5674.515  sq.  ft. 

9.  254.469  sq.  rd. 

10.  452.39  sq.  ft. 

11.  452.39  sq.  rd. 
IS.  804.249  sq.  yd. 

13.  17A.107.44sq.rd. 

14.  50A.148.70sq.rd. 

15.  33.183sq.  ft. 

16.  151.83  sq.  ft. 

17.  3  sq.  ft.  70.65  sq.  in. 
in. 

18.  97.482  sq.  ft. 

Art.  206,  p.  IU 

1.  $12.80 

2.  44  sq.  yd. 

3.  Floor,    etc.,    105 J 
sq.  yd. ;  walls,  59j 
sq.  yd. 

4.  108i  sq.  yd. 

5.  $27.11 

6.  $39.60 

7.  9350  sq.  yd. 

8.  532 


9.  1344  sq.  yd. 

10.  464  sq.  yd. 

11.  $670 

12.  36f  sq.  yd. 

13.  145J  sq.  yd. 

14.  $114.64 

15.  $4833.89 

16.  3019. 077  sq.  ft. 

17.  472$  sq.  yd. 

18.  21  f  squares 

19.  160  sq.  yd. 
SO.  1020  sq.  ft. 

Art.  208,  p.  115 
1.  12 
S.  15 

3.  10 

4.  25 

5.  12 

6.  104yd. 

7.  541^  yds. 

8.  23J 

Art.  209,  p.  117 

1.  $61.60 

*  72  or  69. 80 

3.  Lengthwise, 
$64.80; 
crosswise,  $64 

4.  49yd. 

5.  (a)  186§  yd.  cross- 

wise, 

(b)  50    yd.   cross- 
wise, 

(c)  136  yd.  length- 
wise, 

(d)  21 1  yd.  cross- 
wise, 

(e)37j  yd.   cross- 
wise 

6.  (a)9iyd., 
(b)ljyd., 
(c)8yd., 
(d)3jyd., 

(e)  4f  yd. 


ANSWERS 


289 


7.  (a)86f  yd., 

Art.  219,  p.  122 

7.  1481^  gal. 

(b)  77  yd., 

1.  (a)H>U, 

£.  63.9744  bbl. 

(c)  26  yd., 

(b)  5i, 

9.  18||  gal. 

(d)  32  yd., 

(c)  li, 

20.  1.652  gal. 

(e)  83j  yd. 

22.  15.9936  gal. 

Art.  213,  p.  118 

(e)7j 
2.  $23.63 

12.  239f*gal. 
25.  82.318  bbl. 

1.  (a)2304cu.  ft, 

3.  96  ft. 

(b)784cu.  ft, 

4.  4$  ft. 

Art.  225,  p.  126 

(c)2560cu.  ft, 

2.  115.2  bu. 

(d)  1233  ou.  ft. 

Art.  222,  p.  123 

2.  65|  bu. 

2.  200  cu.  ft. 

2.  20 

3.  llS^bu. 

3.  1344  cu.  ft. 

2.  10i 

4.  $76.56 

4.  5939.886  cu.  ft 

3.  15 

5.  800  cu.  ft.,  25  ft. 

5.  1200  cu.  ft. 

4.  25 

6.  4^  ft. 

6.  2781.  173  cu.  ft. 

5.  32 

7.  117.81  cu.   ft,883.57a 

7.  114648.596  cu.  ft. 

6.  11 

gal. 

7.  6 

8.  6.565  ft 

Art.  214,  p.  119. 

8.  15j 

9.  340£  bu. 

2.  (a)  197.92  cu.  ft, 

9.  26| 

20.  Sll^bu. 

(b)  298.414  cu.  ft., 

10.  42 

22.  47Jbu. 

(c)326.726cu.  ft, 

22.  46f 

22.  87j  bu. 

(d)  982.62  cu.  ft 

22.  162 

13.  1  H  ft. 

2.  2513.28  cu.  ft. 

13.  106f 

14.  62fcwt 

3.  436.72cu.  ft. 

24.  16 

15.  14f£  T. 

4.  26507.25  cu.  ft. 

15.  12 

16.  10  T. 

5.  30.968  cu.  ft. 

2S.  18| 

27.  $162.85 

6.  8.84ft 

27.   10 

2£.  67|J  ft. 

Art.  217,  p.  120 

18.  $5.53 

29.  640  cu.  ft.,  4f  ft 

2.  1050  cu.  ft. 

29.  $63 

£0.   194$  bu. 

2.  $59.05 
3.  $36.27,  cost  of  dig- 
ging; $58.83,  cost 
of  wall  ;  10^5j  cd. 

20.  $25.05 
£2.  $130.65 

22.  $32.82 
23.  $21.20 

Art.  231,  p.  132 

2.  24 

2.  75 

4.  2404  cu.  ft. 

Art.  223,  p.  125 

3.  206 
4.  1234 

5.  12  1  cd. 

6.  27720 

2.  (a)  808.  57 

5.  2.645 

7.  Cost   of    digging, 

(b)  20.09 

6.  1.414 

$93.33;  cost  of  lay- 
ing, $64.15;  Bffy 
cd. 

2.  176}  ibu. 

7.  126 
5.  1626.57 

M 

8.  4838 

4.  84|°bu. 

20.  .968+ 

9.  2592  cu.  ft. 

5.  807?^  gal. 

22.  48.989rd 

10.  $148.78 

6.  79  ;  £  bbl. 

22.  125 

290 


ANSWERS 


13.  38809 

P.  136 

S.  $18,  $21.60 

14.  $397.60 

1.  176.  715  sq.  ft. 

3.  $63 

15.  26.92  ft. 

2.  257.8  sq.  ft. 

4.  $47.40 

107.7  ft. 

3.  24f  ft. 

5.  .75 

Art.  232,  p.  133 

4.  390H  bu. 

6.    25 

1.  419.98  sq.  ft. 

5.  8T5g-cd. 

7.  1200 

S.  9  A.  47.914  sq.  rd. 

6.  132.53  cu.  in. 

8.  $1440 

S.  1200  sq.  ft. 

7.  164.93  sq.  ft. 

9.  500 

4.  2  A.  111.  155  sq.  rd. 

8.  $320.89 

10.   .25 

5.  14.273  rd. 

9.  $392.89 

11.  .125 

6.  1664.45  sq.  ft. 

10.  2035.75+cu.  ft. 

12.  40.48 

7.  45.13  rd. 

11.  21120 

IS.  5,  500 

8.  31.7rd. 

1*.  83^  yd. 

14.  625 

0 

9.  3.19  ft. 

15.  8750  Ib. 

15.  5lf 

10.  309.74sq.  rd. 

14.  168ft. 

16.  252 

11    Circle,   795.77  sq. 

15.  2361.28ft. 

17.   .12 

yd.  ;    square,    625 

16.  1060  cu.  ft. 

18.  .92 

sq.  yd. 

17.  238H  toads 

19.  1.12 

IS.  13.541ft. 

IS   47.1!  bbL 

#0.  .30 

13.  88.622  ft. 

19.  $6!55 

SI.  .08 

14.  6.684ft. 

£0.  130|  sq.  yd. 

0*.  618.75 

15.  9  A.  137.  9  sq.  rd. 

SI.  72j-Jcd. 

23     86 

16.  17  ft.  8  in. 

SS.  48486 

&£    $51 

17.  191.33  sq.  yd. 

0*.  63ft. 

05.  301 

18.    110.84  bu. 

0£  5016  ft.,  209  posts 

Art.  251,  p.  142 

19.  6196.77  sq.  ft. 

25.    168|bu. 

1.  86.4,  446.4,  273.6 

SO.  239.24  sq.  ft. 

26.  (a)  288  ft. 

S.  $294,  994,  406 

Art.  234,  p.  135 

(b)  1104  ft. 
(c)  2520  ft. 

3.  $548.10,  1388.10, 
291.90 

1.  9yd. 

(d)  120  ft. 

4.  $632.875,  1395.375, 

S.  25  ft. 

(e)  1877J  ft. 

129.625 

3.  7  A.  56  sq.  rd. 

(f)  3645  ft. 

5.  $158.77,  696.97, 

4.  31.112ft. 

(g)  2862  ft. 

379.43 

5.  26.076  ft. 

(h)  1842.4  ft. 

6.  $171.10,  855.50, 

6.  19.31  ft. 

(i)  526  sq.  yd. 

513.30 

7.  75ft. 

(j)  $27.84  ' 

7.  $699.45,  1632,05, 

8.  22500  sq.  ft. 

27.  (a)  1780  cu.  ft. 

233.15 

9.  105.47ft. 

(b)  13ft  cd. 

8.  $212.87,  851.47, 

10.  18.7  ft. 

(c)  815  A-  loads, 

425.73 

It  1.414ft. 

(d)  112  sq.  yd. 

9.  $8517.25,  18251.25, 

IS.  1536  sq.  ft. 

(e)  748  sq.  ft. 

1216.75 

13.  150  ft. 
14.  28.42  ft.  , 

Art.  235,  p.  139 

10.  $832,  2080,,  416 
11.  105,  945,  735 

15.  470.3  sq.  ft. 

1.  20,  182J,  504 

IS.  354,  1298,  590 

ANSWERS 


291 


13.  $42732,  2991.24, 

21.  97TV$ 

Art.  255,  p.  149 

2136.60 

00.  .0005  jg$ 

1.  1800 

14.  3924.48,  8596.48, 

2S.  53^$ 

0.  $284.88 

747.52 

04-  ^\% 

5.  882T6T 

15.  $398.95 
16.  6995.  08^ 

Art.  253,  p.  145 

4.  $497.14 
5.  $876.46 

17.  8525 

1.  62400 

0.  1200 

18.  $330.13,  1251.43, 

0.  $135.625 

7.  $404.53 

351.17 

5    1416 

8.  $122.74 

VJ.  $397.39,  1147.19, 

4    ll 

9.  $275.85 

352.41 

5.  4060.15+ 

10.  2100 

20.  1301.44,  5949.44, 

6.  1650000 

11.  1909.556  Ib 

3346.56 

7.   111854 

12.  140.2yd. 

21.  546 

S    12g 

13.  110.731b. 

22.  6  T.  716  Ib. 

9    .0378$ 

14.  400 

2S.  11.28  gal. 

10.  93000000 

15.  $1030.93 

24.  87  T. 
25,  5.46^  yd. 
26.  18.306  Ib. 

11.  $35812.50 
12.  $1172958.46 
IS.  $13861111.11 

Art.  256,  p,  152 

1.  $1063.59 

27.  .1681b. 

14.  $27500 

0.  llyr 

Art.  252,  p.  143 

15.  5170H-  gal. 
10.  2857lf  Ib. 

3.  12if  $ 
4.  $3.834 

1.  &>\% 

17.  400000  gr. 

&•  ^TT9"§"$ 

3.  75$ 

18.  $9166.67 
19.  1578if  Ib.  silver, 

6.  5.48fr* 

7   $140.  62^ 

4-  11$ 

1263T3¥lb  tin, 

&  HTT$ 

5.  60|f  $ 

16736  jf  Ib.  copper 

9.   13H^ 

6.  150$ 

20.  326^-  Ib. 

10.  3lJ$ 

7.  25$ 

11.  25^ 

8.  133j$ 

Art.  254,  p.  147 

10.  3.384$ 

9.  75iW# 

1.  888f 

15.  $7043.75 

fe/.   .06ff$ 

0.  1600 

14.  40$ 

11.  3333|$ 

3.  $26 

15.  63T\$ 

10.  4$ 

4-  446y6o33 

16.  16f? 

IS.  242  |f  $ 

5.  64.224+ 

17.  6f$ 

14.  3?A  $ 

6.  $1219.23 

IS.  60^ 

15.  1580$ 

7.  $1311.69 

19.  $40.19 

16.  99.156+2 

8.  757.696+ 

00.  $4 

17.  2.414+$ 

9.  $469.56 

01.  4$  • 

1*.  831J.11 

10.  $1193  74 

00.  6i$  loss 

19.   .004985+%,     ' 

11.  684 

2S.  $3.4l| 

.006186+$, 

10.  $1600 

04.  $3 

.007123+$ 

13.  251VTlb. 

Art.  2  71,  p.  158 

20.  7.84$,  32H$, 

14-  17.8875  ft. 

1.  Com.,  $19.70; 

59|$,  6.641b. 

1C.  $9259.26 

cost,  $895.30 

292 


ANSWERS 


2.  Com.,  $30.  21; 

18.  Com.,  $17.06; 

10.  (a)  $94.08 

cost,  $984.21 

guar.,  $3.41; 

(b)  $436.30 

3.  Com.,  $8.10; 

proceeds,  $320.78 

(c)  $71  52 

guar.,  $.81; 

19.  $2653 

(d)  $449.75 

cost,  $332.91 

20.  $14610 

(e)  $948.49 

4.  Com.,  $37.96; 

21.  $661.68 

(f)  $2383.  78 

guar.,  $12.65; 

22.  $1123.09 

(g)  $2991.96 

cost,  $1316.01 

2S.  $2932.50 

(h)  $318.05 

5.  Com.,  $70.81; 

24.  $7125.00 

(i)  $499.80 

guar.,  $19.31; 

25.  $5975.65 

(j)  $636.53 

cost,  $1398.75 

26.  $2418.33 

11.  (a)  60% 

6.  Com.,  $35.28: 

27.  $1467.72 

(b)38f% 

guar.,  $5.04; 

28.  $11000 

(c)  43f  % 

cost,  $544.34 

29.  $7266.67 

(d)  20% 

7.  Com.,  $86.25; 

SO.  $18150 

(e)  68|% 

guar.,  $40.02; 

SI.  $5700 

(f)  108  £% 

cost,  $2127.27 

32.  2ff  % 

(g)  66f% 

8.  Com.,  $13.11; 

33.  5% 

(h)  13  \% 

guar.,  $8.74; 

S4.  §\% 

(i)  100% 

cost,  $472.67 

35.  6^"5"  % 

(j)  5^4% 

9.  Com.,  $9.14; 

36.  Com.,  $374.56; 

12.  Firstl^ 

cost,  $313.94 

guar.,  $46.82; 

Art.  276,  p.  165 

10.  Com.,  $30.35: 

proceeds,  $4233.62 

1.  has,  aas,  dhm. 

proceeds,  $836.90 

37.  $6320.05 

hem,  aos,  ms,  no, 

11.  Com.,  $2.42; 

S8.  $2781.13 

his,  nnn,  dns 

guar.,  $.24; 

39.  $479.15 

S.  $1.55,  $5.70,  $.99, 

proceeds,  $94.09 

40.  $1418.27 

$2.18,  $3.65,  $4.25, 

n.  Com.,  $1.28; 

41.  $3515.24 

$8.00,  $7.20,  $12.75 

guar.,  $.32; 

42.  $5809.15 

3.  hid,  m  h  n,  had, 

proceeds,  $62.64 

43.  $99.25 

amn,  dso,   snh 

IS.  Com.,  $123.98; 
proceeds, 

44.  $14070.99 
45.  Second  agent  by 

hyyy»  iyv, 

hsld 

$2975.62 

\% 

Vl    Q   V 

14.  Com.,  $91.27; 

Art.  2  74,  p.  162 

X            V             II         D         J 

r'         wcc 

guar.,  $27.88; 

proceeds, 

1.  $49.94 

(b)  — 

$1706.65 

2.  $445.50 

e  r 

15.  Com.,  $1523.44; 

3.  $708.75,  $725.76, 

hms 

proceeds,  $4489.06 

$696.15 

h  a  a 

16.  Com.,  $520.96; 

4.  $23.60 

,^  a  d  y 

guar.,  $71.04; 

5.  $489.60 

'  h  i  s 

proceeds,  $1776 

6.  $10 

.has 

17.  Com.,  $132.62; 

7.  $7.35 

'  w  r  i 

guar.,  $18.42; 

8.  $351.47 

/f)  ayy 

proceeds,  $534  26 

9.  §1% 

'  h  a  s 

ANSWEB8 


293 


hoy 

I  1st,  $750.66; 

94.  8V 

™hs  s 

2d,  $1154.60; 

55.  $53.75 

/u\    *y 

8d,  $1867.82 

36.  $2.20 

*  '  wsp 

6.  1st,  $3302.18,  pre- 

57. $4.71 

r.v  hay 

miums  ; 

55.  $10.08 

W  hws 

2d,  $3923.60,   pre- 

50. $16.59 

/  -\  h  d  7 

miums  ; 

40.  $37400 

w  o  li 
Art.  280,  p.  166 

8d,  $6347.25,   pre- 
miums; $4617 

P.  181 

1.  $1.46 

1.  $598.93 

received 

0.  61? 

0.  $354.63 

P.  179 

5.  78? 

3.  $996.07 

1.  $9.52 

*  $15.23 

4.  $160.90 

2.  $2.28 

5.  $4.77 

5.  $70.89 

S.  $5.34 

6.  82.53 

£.  $61.84 

4.  $10.56 

7.  $5.37 

7.  $207 

5.  $1.51 

8.  $9.70 

8.  $113.54 

6.  $1.19 

0.  84? 

0.  $13.36 

7.  63? 

10.  94? 

;0.  $19.60 

8.  $14.06 

11.  $2.47 

P.  171 

0.  $13.91 

10.  $8.24 

10.  $17.44 

13.  $3.15 

/.  $41.56 
0   $27126.93 
5.  $189776.67 

11.  $161.97 
12.  $7.16 

15.  $17.22 

14.  75? 
15.  $1.74 
16.  $1.84 

4.  $6.48 

14.  $74.62 

17.  $1.05 

5.  $18.23 

15.  $29.93 

18   S3  32 

5.  $3053.81 

16.  $267.38 

10.  $2.23 

7.  $7275 
5.  $3690.93 
0.  $100260,  loss  to 

17.  $20.63 
W.  $33.69 
19.  $1.29 

00.  44? 
21.  $1423.81 
00.  $1001 

Co.  ;  $43615  loss  to 
owner  under  aver- 

00. $2.42 
21.  $144.87 

05.  $278.05 
94.  $317.94 

age  clause 
10.  $22.  50  per  $1000 
11.  44f  yr. 

00.  $16.13 

05.  $4.22 
04.  $2.77 

05.  $279.14 
26.  $829.57 
07.  $419.22 

12.  8.79^ 
13.  $700.62  and 
$774.38 

05.  $37.66 
26.  $1.39 
07.  $58.09 

28.  $618.13 
00.  $284.59 
50.  $116.25 

P.  176 

05.  $66.82 

SI.  $786.97 

2.  $91.06,    premium: 

00.  $160.09 

50.  $574.60 

$820.06  loss 

50.  $7.55 

55.  $1827.93 

3.  Receive  $2000; 

SI.  $2.42 

54.  $68.22 

would  have  re- 

50. $26.41 

55.  $14800.46 

ceived  $1703.34 

33.  $12.91 

86.  $844.29 

$94 


AKSWEBS 


37.  1207.84 

38.  §259.73 

39.  §359.11 
M.  £674.66 


1. 


S.  §1.88 

£  §10.37 

5.  §22.64 

6.  §8.62 

7.  §97.51 
S.  $57.99 
9.  §146,41 

10.  §25.59 

11.  §24.29 
^  §6.21 

15.  §6.91 
14.  §175.07 
J5.  §17.93 

16.  §2.90 

17.  $10.35 

18.  §5.84 

19.  $231.30 
m  $66.18 


84. 


§2.63 
§8.16 

§12.24 
85.  $19.42 

26.  §1.11 

27.  §1.51 
2S.  §4.86 
89.  $6.87 

30.  $7.70 

P. 

31.  56^ 
52.  §1.49 
55.  §3.05 
5£  $4.29 
25.  #1.82 
50.  $5.61 
§7.  $1.13 


$8.  11.19 

59.  §34.96 

40.  §31.85 

P.  185 

&  §17.59 

5.  §6.60 

4.  $.18 

5.  §62.48 

0.  §35.93 
7.  $19.66 
5.  $6.26 
9.  $2.63 

10.  $8.67 

P.  186 

1.  $51.75 


5.  §24.10 

4.  §156.60 

5.  §40.64 
0.  §14.53 
7.  $29.98 
5.  §9.59 
9.  §25.28 

10.  §27.67 
Zl.  §59.85 

18.  §139.50 
*5.  §3.18 

14.  $4.29 

15.  §14.73 

16.  $9.59 

17.  §9.24 
15.  §6.55 

19.  §1.51 

20.  §3.63 
'£1.  $22.09 
88.  §40.4£ 
25.  §66.22 
84.  §126.02 

25.  §79.04 

26.  §259.72 

27.  $225.16 
88.  $115.77 


89.  $73.37 

50.  §131.84 

51.  §246.02 

58.  §172.83 

55.  $21 

54.  §261.36 
55  §30.76 

56.  §12.22 
37.  §61.57 

55.  §108.25 

59.  §55.87 
40.  §152.64 

P.  187 

t  $2090,  $663.90 
&  §22=50,  §740.50 

3.  §3.05,  §139.05. 

4.  §9.11,  $216.11 

5.  §39.25,  §1731.25 
0.  $45.35,  §2091.35 

7.  §1.76,  §252.76 

8.  $3.24,  §238.24 
P.  §94.46,  §2281.46 

10.  §14.01,  §528.01 

11.  §54.86,  §396.86 
18.  §31.59,  §665.59 

13.  §74.29,  §812.29 

14.  §51.15,  §1286.15 

15.  §133.73,  §3083.73 

16.  §80,38,  §1045.68 

17.  §6.98,  §439.98 

18.  §23.48,  §1603.48 

19.  §64.17,  §939.17 

80.  §41.86,  §427.86 

81.  §43.59,  §958.59 

82.  §110.80,  §1133.80 
8S.  $238.66,  $3845.66 

84.  §59.75,  §678.75 

85.  §54.17,  §839.17 

86.  §2.31,  §317.31 

87.  §3.44,  §430.44 

88.  §10.58,  §1390.58 
25.  §14.12,  §1039.12 
50.  $7.24,  $723.24 
31.  $10.03.  §834.03 


ANSWERS 


296 


51  $3.74,  $909.74 
S3.  $3.84,  $317.84 
34-  $8.06,  $431.06 

P.  188 

35.  45?,  $206  45 

86.  $3.56,  $344.56 

37  $10.53,  $1227.53 

38,  $11.82,  $1098.82 

99.  $4.75,  $425.75 

40.  $3.77,  $541.77 

41.  $8  04,  $681.04 

42.  $2.03,  $740.03 
43  $1.62,  $298.62 

44.  $4.02,  $313.02 

45.  $5.32,  $278.32 

46.  $7.23,  $955.23 

47.  $49.90,  $3120.90 

48.  $34.44,  $4287.44 
45.  $29.37,  $1435.37 
50.  $36  72,  $2386.72 

Art.  328,  p.  188 

1.  $4.80 

2.  4  mo. 

3.  §% 

4.  $374.40 

5.  6^ 

5.  8  mo. 

7.  $360 

8.  4  yr.  2  mo. 

10.  8  mo.  5  da. 

11.  16-Jyr.,  20yr.,12j 
yr.,  33j  yr.r  14f 
yr.,  10  yr. 

12.  ±\% 

13.  3  yr.  4  mo.  27  da. 

14.  $537.04 


16.  1  yr.  2  mo.  22  da. 

18.  $904.98 
10.  22f  yr. 


Art.  335,  p.  191 

5.  Due  date,  April  8( 

1.  $147.82 

8728.44 

2.  $43.33 

£  Due  date,  May  13 

3.  $77.50 

$599.36 

4.  $154.25 

£.  Due  date,  June  7, 

5.  $138.06 

1900,  S297.44 

6.  $149.34 

6.  Due  data,  Oct.  3> 

7.  $139 

1898,  551278.85 

8.  $589  88 

7.  Due  date,  July  4, 

S.  $330.80 

1898,  $381.30 

10.  $368.02 

8.  Due  date,  Pec.  28, 

11.  $178.05 

$234.72 

12.  $533.98 

9.  Due  date,  Nor.  29, 

13.  $453.06 

$4217.90 

10.  Due  date,  Dec.  30 

Art.  337,  p.  192 

$551.01 

1.  $129 

11.  Due  date,  Dec.  1, 

2.  $132.55 

$348.21 

5.  $74.64 

12.  Due  date,  May  8 

4.  $883.15 

$438.32 

5.  $144.29 

'ft  $697.97 

Art.  361,  p.  202 

7.  $159.27 

1.  $292.40 

5.  $469.22 

2.  $289.04 

3.  $595.51 

Art.  338,  p.  193 

4.  $367.29 

1.  $681.88 
2.  $1002,05 

Art.  362,  p.  204 

3.  $1002.80 

1.  $1549.55 

4>  $314.36 

2.  $527.86 

5.  $377.95 

3.  $1213.01 

6.  $4097.36 

4.  $174 

7.  $1243.53 

5.  $1353.51 

5.  $1622.84 
9.  $1265.59 

Art.  363,  p.  206 

10.  $1594.59 
11.  $141.87 

1.  $1051.92 
2.  $1912.37 

IS.  $181.81 

3.  $219.40 

13.  $1353.14 

4-  $853.05 

14.  $380.25 

5.  $1597.33 

15.  $642.21 

6,  $312.86 

7.  $934.37 

Art.  359,  p.  200 

*.  $1735.54 

1    $269.08 

9.  $623.72 

2    $512.32 

10.  $1373.82 

296 


ANSWERS 


Art.  366,  p.  208 

1.  8807.69 

2.  $1193.89 

3.  Present  worth, 

$1204.95  ; 
discount,  $12.05 

4.  Present  worth, 

$578.37; 
discount,  847.43 

5.  Present  worth, 

$2928.47; 
discount,  $155.5? 

6.  Present  worth, 

$196.94; 
discount,  $18.31 

7.  Present  worth, 

$1016.15; 
discount,  $11.85 

8.  Present  worth, 

$1906.25; 
discount,  $228.75 

9.  Present  worth, 

$599.16; 

discount,  $116.84 
10.  Present  worth, 

$867.59; 

discount,  $69.41 
11    $1245.02 

12.  $3556.60 

13.  $1266.98 

14.  4^  gained  on  each 
by  buying  on  time 

15.  Time  offer  $23.81 
better 

16.  $2500 

17.  $15.31  gain 

18.  19.23^ 

19.  Cash  offer  is 
$11.  54  better 

SO.  $6124.95 
21.  $8333.33 


23.  $110.57 
£4.  $3162.98 


Art.  374,  p.  213 

Art.  390,  p.  218 

Disc.     Proceeds 

1.  $121.82 

1.  $  8.24    $  184.22 

2.  $71.33 

2.       1.56        223.44 

#.  $399.38 

3.       5.00        436.45 

4.  229.16 

4.       6.59        253.41 

5.  $131.84 

5.       2.37        709.63 
6.       3.65        452.35 

Art.  395,  p.  22S 

7.       4.52        577.19 

1.  $851.70 

8.       4.30        326.59 

&  $1283.20 

9.      6.56        485.72 

3.  $3803.04 

10.       3.98        314.02 

4.  $1571.57 

11.     10.41        640.26 

5.  $9709.70 

12.     13.07        527.68 

6.  $3260.92 

13.     17.79       1142.21 

7.  1st,  $1.002  ;2d,  $5 

14-      6.19        475.93 

3d,  $850 

15.      1.23        327.77 

8.  $2506.27 

16.     19.65       1280.85 

9.  32^ 

17.      6.23        731.77 

10.  $4491.02 

18.      2.70        423.30 

Art.  398,  p.  224 

19.      4  69        375.31 

1.  $2305.75 

20.      7.13         534.65 

2.  $18227.19 

21.      4.20        835.80 

S.  $6580 

22.      2.21        234.79 

4.  §753.40 

Art.  385,  p.  216 

5.  $1592.93 

1.  $337.17 

6.  $1692.42 

2.  $246.25 

7.  $3780.52 

3.  $471.83 

8.  $1260 

4.  $594 

9.  $537.46 

5.  $845.75 

10.  2522.52 

6.  $1188 

Art.  401,  p.  225 

7.  $397.33 

1.  $199.50 

8.  $357.60 

2.  $177.75 

9.  $512.20 

3.  $174.12 

W.  $173.98 

4.  $1779.75 

il.  $227.70 

6.  $2333.45 

*£.  $147 

7.  $580.58 

Art.  388,  p.  21  7 

8.  $2380 

1.  $197 

Art.  410,  p.  228 

2.  $345.62 

1.  $2044.60 

3.  Proceeds,  $346.50, 

2.  264  sov.  6s.  8d. 

lack,  3^f  ;  amount 

2  far. 

due,  1352.28 

J.  $606.43 

ANSWERS 


297 


4.  $6937.98 

10.  June  13 

8.  Beekman,  $480; 

5.  $4523.75 

11.  March  16 

Hadley,  $320; 

6.  937  sov.  6s.  Id. 

12.  Balance,  $220; 

Perry,  $440 

3  far. 

Dec.  27,  1899, 

S.  $1500,  $1000 

7.  $3497.40 

$225.68 

4.  Watson,  gain 

8.  Cost,  $4918.38; 

13.  Feb.  19,  $216.47 

$1292.31;  P.  W., 

face,  $4900 

15.  $1.43,  interest  due 

56892.31;    Barnes, 

9.  $20281.40 

April  25 

gain  $1507.  69; 

10.  $38528.44 
Art.  420,  p.  232 

Art.  436,  p.  248 

1.  $157.59 

P.  W.,  $7807.69 
5.  A,  $5400;  B,  $8100; 
C,  $6750;  D,  $9450 

1.  $5.23 
8.  $410.80. 

8.  $41.21 
S.  $159.64 

6.  Gooding, 
$22193.68; 

S.  $899.88 

4.  $22.38 

Spencer,  $17966.32 

4.  $186.80 

Art.  441,  p.  249 

7.  Ha  wes  owned  yV  ; 

P.  233 

1.  $288.86 

8.  $586.65,  due  Dec. 

12 

Gross,  T5s  ;  Ha  wes 
received  $23333  J; 

8.  $3607.50 
3.  $455.56 

4.  $811.42 

J./Q 
1.  $1417.48 
S.  $1399.40,  due  Aug. 

Cross,  $16666|  ; 
Hawes  received 
$26666f 

5.  $2116.80 

20 

9.  Martin,    $190328; 

6.  $131.21 

Art.  442,  p.  251 

Gould,  $1480.33; 

7.  $206.79 

1.  A,  $6;  B,  $8 

Towne,  $1776.39 

8.  $767  64 

8.  1st,  $15;  2d,  $25 

10.  Howe,  $470.14; 

9.  $232.23 

3.  10,  20,  30 

Benton,  $428.72; 

*ft  $323.72 

4.  60,  72,  84 

Ward,  $351.14 

Art.  431,  PC  240 

5.  150,  225,  375 

11.  Bush,  $104.35; 

1.  Feb.  25 

6.  A,  $240;    B,  $420; 

Austin,  $208.69; 

2.  March  11 

C,  $510 

Fox,  $86.96 

3.  May  30 

7.  A,  A;  B,  T^;  C, 

12.  Johnson,  $1033  J; 

4.  July  6 

•3*3-;  A's  gain,  $50 

Chapin,$466| 

5.  Aug.  9 

8.  A,  $75;  B,  $135 

13.  Wright,  $13645.  18  ; 

6.  Sept.  4 

9.  $150,  $175,  $225 

Greene,  $11574.01; 

7.  Oct.  19 

10.  45,  30 

Bates,  $14590.15; 

5.  Oct.     2 

U.  45,  27 

Thompson, 

18.  210,  «60 

$6190.66 

Art.  432,  p.  242 

13.  225,  400,  480 

14.  Randall,  $7865.89 

1.  Dec.  21 

74.  $103.25,  §92.75, 

Chapman, 

#.  May  25 

$177.10 

$8125.92    Holt, 

3.  Aug.  6 

15.  $120,  $135,  $150 

$6508.19 

5.  Jan.  4,  1901 

5.  March  27 

Art.  456,  p.  253 

Art.  471,  p.  259 

7.  March  23 

1.  Jones,  $980; 

1.  $288 

£.  Feb.  4 

Smith,  $700; 

2.  $460 

£.  June  2 

Brown,  $1260 

S.  $801 

298 


ANSWERS 


4. 

8206 

Art.  490,  p.  268 

11. 

§\% 

5. 

,  5i#                                1.  8208.13,  817.68, 

12. 

2299.  12  sq.  ft. 

6.  2-gft> 

8273.56,  85.51, 

13. 

24856^  mi. 

7. 

6  \  %  above  par 

83.51.  81.46,'  82.05, 

14. 

213  T.  1650.3  ?b. 

8.  814328.13 

82.59,  852.61, 

15. 

81368.89 

9. 

830220.25 

825.20,  8156.38, 

16. 

33.941  rd. 

10. 

85773.75 

8104.06 

.  7. 

42  57  rd. 

11. 

88385 

2. 

Rate,  .0053; 

18. 

11.653  rd. 

12. 

81020 

865.69,  824.17, 

19. 

14.142  in. 

13. 

812578.13 

838.56,  8131.92, 

20. 

842857.14 

u. 

810046.25 

8228.56 

21. 

20.67^ 

16. 

56 

3. 

(a)  818.10 

22. 

Increased  855 

17. 

28 

(b)  87.31 

23. 

81173.54 

18. 

48 

(c)  85.90 

24. 

84485.61 

19. 

8^V  premium 

(d)  817.  28 

25. 

15033T3T  Ib 

21. 

8896 

(e)  86.48 

26.  2  yr.  9  mo.  18  da. 

22. 

8320 

4> 

.00745 

27. 

720.28 

23. 

8672 

5. 

.008065 

28. 

1.135%  loss 

24. 

First  $17.50 

6. 

86403 

29. 

Gain,    82405; 

P 

25. 

Increased  $> 

7. 

8116.47 

W.,  810405 

26. 

135 

8. 

822.97 

30. 

834.24 

27. 

28. 

814445 
820146.88 

Art.  506,  p.  270 

32. 

8513.75 

8647.07 

?9. 

840026.25 

1. 

$835.80 

AQ-f  O 

33. 

Oct.  3 

SO. 

834200 

2. 

5fol4 

34- 

(a)  81021.  36 

91. 

1% 

3. 
i 

88828 

(b)  81021.10 

33. 

5~t  % 

4- 

$tt 

35. 

Gain,  82355; 

94 

1\% 

5. 

88350.70 

resources,  89225 

35. 

Latter  \\% 

6. 

8188.70 

liabilities,  86870 

142f 

7. 

867.13 

P.  W.,  $7355 

88. 

96 

8. 

815480 

36 

166f# 

14f% 

9. 

$659.32 

37. 

27.325% 

40. 

10. 

8840 

38. 

847.58 

Art.  474,  p.  264 

P.  272 

39. 

836.75 

1. 

8 

40. 

892.62 

2. 

$292.95 
$4315.72 

3. 

19  T,  57lf  Ib. 
.  3515.6  Ib. 

41. 

14T6T  ft. 
.0375 

3. 
4. 

$86.47 
$4900 

5. 

32400  Ib. 
833.10 

43. 

44- 

8  breadths,  42-|  yd. 
8348 

Art.  489,  p.  267 

6. 

10  rd.  3  yd.  2  ft. 

45. 

10368 

L 

882.40 

7. 

4ftf 

46. 

46^ 

2. 

8260.63 

8. 

1737.59  gal. 

47. 

8205 

$. 

.0074,  822.05, 

9. 

81000 

48. 

34.22% 

$272.84 

10. 

8119.65 

49.  Ill  bu.  1  pk.2J  qt. 

ANSWERS 


60.  $390 

51.  $30 

52.  $76613 

53.  58}  ib. 
54. 

55. 


57.  $10875 
55.  45932jf 
59.  $17840 
£0.  5.86^ 
01.  70$  it. 
6*2.  $5.75 

6£.  702  Ib.  copper, 
198  lo.  tin. 


64.  $2420 

65.  7  T.  1384  Ib. 

66.  §{% 

67.  $14.50 

68.  75 

69.  $185.96 

70.  8.8T\# 

71.  $58.65 

n.  $3:84 

75.  $412 

7&  A,  $17671.8)- 

B,  $23557.24 

C,  $7933.85, 

D,  $18837.10 
7J,  $100.38 


76.  7.48?* 

77.  (a)  37.57^ 

(b)  14.66^ 
(e) 

(c)  17. 1 
(j)  2.4 

75.  51b.  at  14?;  3  Ib 
at  W;  4  Ib.  at 
25^:  4  Ib.  at  32^, 
666|  Ib. 

79.  $15.94 

80.  $673.96 


T.. 


THIS  BOOK  IS  DUE  ON  THE  LAST  DATE 
STAMPED  BELOW 


AN  INITIAL  FINE  OF  25  CENTS 

WILL  BE  ASSESSED  FOR  FAILURE  TO  RETURN 
THIS  BOOK  ON  THE  DATE  DUE.  THE  PENALTY 
WILL  INCREASE  TO  5O  CENTS  ON  THE  FOURTH 
DAY  AND  TO  SI.OO  ON  THE  SEVENTH  DAY 
OVERDUE. 


2  1934 


MAR    26  1934 


301049 


+< 


20Dec'59JO 

REOD  LD 

DEC  6  -  1959 

LD  21-100 


V8  '1 7244 


X 

.  / 


' 


